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Selected

  1. D. Li, Global well-posedness of hedgehog solutions for the (3+1) Skyrme model. Duke Math. J. 170 (2021), p.1377–1418. pdf
  2. X. Cheng, H. Kwon, D. Li, Non-uniqueness of steady-state weak solutions to the surface quasi-geostrophic equations. Comm. Math. Phys. 388 (2021), p.1281-1295. pdf arXiv:2007.09591.
  3. D. Li, C. Quan, T. Tang, Stability and convergence analysis for the implicit-explicit method to the Cahn-Hilliard equation. Math. Comp., (2022) 91(334): 785-809. pdf
  4. D. Li, Effective maximum principles for spectral methods. Ann. Appl. Math., 37 (2021), p. 131–290. pdf
  5. J. Bourgain, D. Li, Strong ill-posedness of the 3D incompressible Euler equation in borderline spaces. Int. Math. Res. Not. IMRN, 16(2021), p.12155–12264. pdf
    (See also https://academic.oup.com/imrn/pages/30years)
  6. D. Li, J. Rodrigo, Remarks on a nonlocal transport. Adv. Math. 374 (2020), 107345 pdf
  7. J. Bourgain, D. Li, Galilean boost and non-uniform continuity for incompressible Euler. Comm. Math. Phys. 372 (2019), p.261–280. pdf
  8. D. Li, On Kato-Ponce and fractional Leibniz. Rev. Mat. Iberoam. 35 (2019), p.23–100. pdf
  9. B. Han, Z. Lei, D. Li, N. Zhao, Sharp one component regularity for Navier-Stokes. Arch. Ration. Mech. Anal. 231 (2019), p. 939–970. pdf
  10. D. Li, Z. Qiao, T. Tang, Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations. SIAM J. Numer. Anal. 54 (2016), p.1653–1681. pdf
  11. J. Bourgain, D. Li, Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Invent. Math. 201 (2015), p. 97–157. pdf
  12. J. Bourgain, D. Li, Strong illposedness of the incompressible Euler equation in integer Cm spaces. Geom. Funct. Anal. 25 (2015), p.1–86. pdf
  13. D. Li, Y. Wu, The Cauchy problem for the two dimensional Euler-Poisson system. J. Eur. Math. Soc. 16 (2014), p. 2211–2266. pdf
  14. D. Li, X. Yu, Z. Zhai, On the Euler-Poincaré equation with non-zero dispersion. Arch. Ration. Mech. Anal. 210 (2013), p. 955–974. pdf
  15. D. Li, Y.G. Sinai, Nonsymmetric bifurcations of solutions of the 2D Navier-Stokes system. Adv. Math. 229 (2012), p.1976–1999. pdf
  16. D. Li, J.L. Rodrigo, X. Zhang, Exploding solutions for a nonlocal quadratic evolution problem. Rev. Mat. Iberoam. 26 (2010), p. 295–332. pdf
  17. D. Li, J.L. Rodrigo, Wellposedness and regularity of solutions of an aggregation equation. Rev. Mat. Iberoam. 26 (2010), p.261–294. pdf
  18. D. Li, J.L. Rodrigo, Refined blowup criteria and nonsymmetric blowup of an aggregation equation. Adv. Math. 220 (2009), p. 1717–1738. pdf
  19. D. Li, X. Zhang, On the classification of minimal mass blowup solutions of the focusing mass-critical Hartree equation. Adv. Math. 220 (2009), p. 1171–1192. pdf
  20. W. E, D. Li, On the crystallization of 2D hexagonal lattices. Comm. Math. Phys. 286 (2009), p.1099–1140. pdf
  21. H. Dong, D. Li, Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations. Arch. Ration. Mech. Anal. 189 (2008), p. 131–158. pdf
  22. W. E, D. Li, The Andersen thermostat in molecular dynamics. Comm. Pure Appl. Math. 61 (2008), p. 96–136. pdf

Preprints

  1. D. Li, J. Li, A global quadratic speed-up for computing the principal eigenvalue of Perron-like operators. arXiv:2111.12642. pdf
  2. D. Li, C. Quan, W. Yang, An F-modulated stability framework for multistep methods. arXiv:2111.05210. pdf
  3. D. Li, K. Yang, On the gap property of a linearized NLS operator. arXiv:2110.14393. pdf
  4. J.F Cai, M. Huang, D. Li, Y. Wang, On smoothed amplitude flow models for phase retrieval. pdf
  5. D. Li, C. Quan, Negative time splitting is stable. arXiv:2107.07332.pdf
  6. D. Li, C. Quan, On the energy stability of Strang-splitting for Cahn-Hilliard. arXiv:2107.05349.pdf
  7. X. Cheng, D. Li, C. Quan, W. Yang, On a sinc-type MBE model. arXiv:2106.16193.pdf
  8. D. Li, Optimal Gevrey regularity for supercritical quasi-geostrophic equations. arXiv:2106.12439.pdf
  9. D. Li, Uniform estimates for 2D quasilinear wave. arXiv:2106.06419.pdf
  10. X. Cheng, D. Li, J. Xu, Uniform boundedness of highest norm for 2D quasilinear wave. arXiv:2104.10019.pdf

All

  1. D. Li, Why large time-stepping methods for the Cahn-Hilliard equation is stable. (to appear in Math. Comp.), (2022) pdf
  2. D. Li, C. Quan, J. Xu, Energy-dissipation for time-fractional phase-field equations. (to appear in Commun. Pure Appl. Anal.), (2022)  pdf
  3. X. Cheng, D. Li, W. Yang, On the equivalence of classical Helmoltz equation and fractional Helmoltz equation with arbitrary order. (to appear in Comm. Contemp. Math.), (2022) doi:10.1142/S0219199722500353
  4. X. Cheng, D. Li, J. Xu, D. Zha, Global wellposedness for 2D quasilinear wave without Lorentz. Dynam. Part. Differ. Eq., 19 (2022), no.2, p. 123-140. pdf
  5. D. Li, A regularization-free approach to the Cahn-Hilliard equation with logarithmic potentials. Discrete Contin. Dyn. Syst., 42 (2022), no.5, p. 2453-2460. pdf
  6. D. Li, Y Sire, Remarks on the Bernstein inequality for higher order operators and related results. (to appear in Trans. AMS), (2022) arXiv:2109.07952.
  7. D. Li, C. Quan, T. Tang, W. Yang, Sharp convergence to steady states of Allen-Cahn. Commun. Math. Anal. Appl., doi:10.4208/cmaa.2022-0005 pdf
  8. J.-F Cai, M. Huang, D. Li, Y. Wang, The global landscape of phase retrieval II: quotient intensity models. Ann. Appl. Math., 38 (2022), no. 1, p. 62–114. pdf
  9. J.-F Cai, M. Huang, D. Li, Y. Wang, The global landscape of phase retrieval I: perturbed amplitude models. Ann. Appl. Math., 37 (2021), no. 4, p. 437–512. pdf
  10. D. Li, C. Quan, J. Xu, Stability and convergence of Strang splitting. Part I: Scalar Allen-Cahn equation. J. Comput. Phys., 458 (2022), No. 111087. pdf
  11. D. Li, C. Quan, J. Xu, Stability and convergence of Strang splitting. Part II: Tensorial Allen-Cahn equations. J. Comput. Phys., 454 (2022), No. 110985. pdf
  12. J.-F Cai, M. Huang, D. Li, Y. Wang, Solving phase retrieval with random initial guess is nearly as good as by spectral initialization. Appl. Comp. Harm. Anal., (2022) 58: 60–84. pdf
  13. D. Li, C. Quan, The operator-splitting method for Cahn-Hilliard is stable. J. Sci. Comput., (2022) 90(1): 1-12. pdf
  14. D. Li, On fractional smoothness of modulus of functions. Ann. Appl. Math., 37 (2021), no. 3, p. 394–404. pdf
  15. X. Cheng, H. Kwon, D. Li, Non-uniqueness of steady-state weak solutions to the surface quasi-geostrophic equations. Comm. Math. Phys. 388 (2021), p.1281-1295. pdf
  16. D. Li, C. Quan, T. Tang, W. Yang, On symmetry breaking of Allen-Cahn. CSIAM Trans. Appl. Math., 3 (2022), p. 221-243. (2021) pdf
  17. J.-F Cai, D. Li, J. Sun, K. Wang, Enhanced expressive power and fast training of neural networks by random projections. CSIAM Trans. Appl. Math., (2021) 2(3): 532–550. pdf
  18. D. Li, C. Quan, T. Tang, Stability and convergence analysis for the implicit-explicit method to the Cahn-Hilliard equation. Math. Comp., (2022) 91(334): 785-809. pdf
  19. D. Li, C. Quan, W. Yang, The BDF3/EP3 scheme for MBE with no slope selection is stable. J. Sci. Comput, (2021) 89:33. pdf
  20. X. Cheng, D. Li, C. Quan, W. Yang, On a parabolic sine-Gordon model. Numer. Math. Theor. Meth. Appl, 14 (2021), p.1068-1084. pdf
  21. J. Bourgain, D. Li, Strong ill-posedness of the 3D incompressible Euler equation in borderline spaces. Int. Math. Res. Not. IMRN, 16(2021), p.12155–12264. pdf
  22. D. Li, Effective maximum principles for spectral methods. Ann. Appl. Math., 37 (2021), p. 131–290. pdf
  23. D. Li, Global well-posedness of hedgehog solutions for the (3+1) Skyrme model. Duke Math. J. 170 (2021), p.1377–1418. pdf
  24. S. Jitomirskaya, D. Li, S. Reich, A.J. Zaslavski, Preface: Dynamical systems, ergodic theory and mathematical physics, Part II. Pure Appl. Funct. Anal., 6 (2021), p.i–ii. pdf
  25. D. Li, T. Tang, Stability of the Semi-Implicit Method for the Cahn-Hilliard Equation with Logarithmic Potentials. Ann. Appl. Math., 37 (2021), p. 31-60. pdf
  26. X. Cheng, D. Li, K. Promislow, B. Wetton, Asymptotic behaviour of time stepping methods for phase field models. J. Sci. Comput., 86(2021), p.1-34. pdf
  27. S. Jitomirskaya, D. Li, S. Reich, A.J. Zaslavski, Preface: Dynamical systems, ergodic theory and mathematical physics, part I. Dedicated to Professor Yakov Sinai on the occasion of his 85th birthday. Pure Appl. Funct. Anal. 5 (2020), p.i–ii. pdf
  28. D. Li, F. Wang, K. Yang, An improved gradient bound for 2D MBE. J. Differential Equations 269(2020), p.11165–11171. pdf
  29. D. Li, J. Rodrigo, Remarks on a nonlocal transport. Adv. Math. 374 (2020), 107345. pdf
  30. D. Li, On some conjectures of Heywood. Pacific J. Math. 306 (2020), p.221–263. pdf
  31. D. Li, X. Zhang, A regularity upgrade of pressure. Contemp. Math., 725 (2019), p. 163–185. pdf
  32. J. Bourgain, D. Li, Galilean boost and non-uniform continuity for incompressible Euler. Comm. Math. Phys. 372 (2019), p.261–280. pdf
  33. T. Hmidi, D. Li, Dynamics of one-fold symmetric patches for the aggregation equation and collapse to singular measure. Anal. PDE 12 (2019), p.2003–2065. pdf
  34. D. Li, K. Wang, Symmetric radial decreasing rearrangement can increase the fractional Gagliardo norm in domains. Commun. Contemp. Math. 21 (2019), 1850059. pdf
  35. L. Guan, D. Li, K. Wang, K. Zhao, On a class of nonlocal SIR models. J. Math. Biol. 78 (2019), p.1581–1604. pdf
  36. D. Li, On Kato-Ponce and fractional Leibniz. Rev. Mat. Iberoam. 35 (2019), p.23–100. pdf
  37. B. Han, Z. Lei, D. Li, N. Zhao, Sharp one component regularity for Navier-Stokes. Arch. Ration. Mech. Anal. 231 (2019), p. 939–970. pdf
  38. D. Li, Z. Qiao, On the stabilization size of semi-implicit Fourier-spectral methods for 3D Cahn-Hilliard equations. Commun. Math. Sci. 15 (2017), p.1489–1506. pdf
  39. C. Boldrighini, D. Li, Y.G. Sinai, Complex singular solutions of the 3-d Navier-Stokes equations and related real solutions. J. Stat. Phys. 167 (2017), p.1–13. pdf
  40. X. Cheng, D. Li, D. Shirokoff, B. Wetton, On the spectral gap of a square distance matrix. J. Stat. Phys. 166(2017), p.1029–1035. pdf
  41. T. Hmidi, D. Li, Small B∞,∞-1 implies regularity.Dyn. Partial Differ. Equ. 14 (2017), p.1–4. pdf
  42. D. Li, Z. Qiao, On second order semi-implicit Fourier spectral methods for 2D Cahn-Hilliard equations. J. Sci. Comput. 70 (2017), p.301–341. pdf
  43. D. Li, Z. Qiao, T. Tang, Gradient bounds for a thin film epitaxy equation. J. Differential Equations 262 (2017), p.1720–1746. pdf
  44. D. Li, Z. Qiao, T. Tang, Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations. SIAM J. Numer. Anal. 54 (2016), p.1653–1681. pdf
  45. S. Le Coz, D. Li, T.P. Tsai, Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations. Proc. Roy. Soc. Edinburgh Sect. A, 145 (2015), p.1251–1282. pdf
  46. D. Li; R. Pan; K. Zhao, Quantitative decay of a one-dimensional hybrid chemotaxis model with large data. Nonlinearity, 28 (2015), p.2181–2210. pdf
  47. J. Bourgain, D. Li, Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Invent. Math. 201 (2015), p. 97–157. pdf
  48. I.J. Jeong, D. Li, A blow-up result for dyadic models of the Euler equations. Comm. Math. Phys. 337 (2015), p.1027–1034. pdf
  49. J. Bourgain, D. Li, Strong illposedness of the incompressible Euler equation in integer Cm spaces. Geom. Funct. Anal. 25 (2015), p.1–86. pdf
  50. H. Dong, D. Li, Global H˙1∩H˙−1 solutions to a logarithmically regularized 2D Euler equation. J. Math. Fluid Mech. 17 (2015), p.1–7. pdf
  51. M. Avdeeva, D. Li, Y.G. Sinai, New limiting distributions for the Möbius function. Mosc. J. Comb. Number Theory, 4 (2014), p.3–51. pdf
  52. D. Li, Y. Wu, The Cauchy problem for the two dimensional Euler-Poisson system. J. Eur. Math. Soc. 16 (2014), p. 2211–2266. pdf
  53. D. Li, Y.G. Sinai, An application of the renormalization group method to stable limit laws. J. Stat. Phys. 157 (2014), p. 915–930. pdf
  54. J. Bourgain, D. Li, On an endpoint Kato-Ponce inequality. Differential Integral Equations, 27 (2014), p. 1037–1072. pdf
  55. D. Li, G. Xu, X. Zhang, On the dispersive estimate for the Dirichlet Schrödinger propagator and applications to energy critical NLS. Canad. J. Math. 66 (2014), p.1110–1142. pdf
  56. Z. Lei, D. Li, X. Zhang, Remarks of global wellposedness of liquid crystal flows and heat flows of harmonic maps in two dimensions. Proc. Amer. Math. Soc. 142 (2014), p. 3801–3810. pdf
  57. D Li, X. Yu, On some Liouville type theorems for the compressible Navier-Stokes equations. Discrete Contin. Dyn. Syst. 34 (2014), p. 4719–4733. pdf
  58. J. Jang, D. Li, X. Zhang, Smooth global solutions for the two-dimensional Euler Poisson system. Forum Math. 26 (2014), p. 645–701. pdf
  59. D. Li, C. Miao, L. Xue, On the well-posedness of a 2D nonlinear and nonlocal system arising from the dislocation dynamics. Commun. Contemp. Math. 16 (2014), 1350021. pdf
  60. H. Dong, D. Li, On a generalized maximum principle for a transport-diffusion model with log-modulated fractional dissipation. Discrete Contin. Dyn. Syst. 34 (2014), p. 3437–3454. pdf
  61. M. Avdeeva, D. Li, Y.G. Sinai, New Erdős-Kac type theorems for signed measures on square-free integers. J. Stat. Phys. 154 (2014),p. 327–333. pdf
  62. H. Dong, D. Li, On a one-dimensional α-patch model with nonlocal drift and fractional dissipation. Trans. Amer. Math. Soc. 366 (2014), p. 2041–2061. pdf
  63. D. Li, On a frequency localized Bernstein inequality and some generalized Poincaré-type inequalities. Math. Res. Lett. 20 (2013), p.933–945. pdf
  64. D. Li, X. Xu, Global wellposedness of an inviscid 2D Boussinesq system with nonlinear thermal diffusivity. Dyn. Partial Differ. Equ. 10 (2013), p. 255–265. pdf
  65. D. Li, X. Yu, Z. Zhai, On the Euler-Poincaré equation with non-zero dispersion. Arch. Ration. Mech. Anal. 210 (2013), p. 955–974. pdf
  66. D. Li, C. Miao, X. Zhang, On the isentropic compressible Euler equation with adiabatic index γ=1. Pacific J. Math. 262 (2013), p. 109–128. pdf
  67. A. Bulut, M. Czubak, D. Li, N Pavlović, X. Zhang, Stability and unconditional uniqueness of solutions for energy critical wave equations in high dimensions. Comm. Partial Differential Equations, 38 (2013), p. 575–607. pdf
  68. S. Dai, D. Li, K. Zhao, Finite-time quenching of competing species with constrained boundary evaporation. Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), p. 1275–1290. pdf
  69. D. Li, X. Zhang, Wave operators for nonlinear wave equations with null structures. Recent advances in harmonic analysis and partial differential equations, Contemp. Math., 581(2012), p. 257–269. pdf
  70. D. Li, Bifurcation of critical points for solutions of the 2D Euler and 2D quasi-geostrophic equations. J. Stat. Phys. 149 (2012), p. 92–107. pdf
  71. N. Chernov, D. Li, Decay of Fourier modes of solutions to the dissipative surface quasi-geostrophic equations on a finite domain. Chaos Solitons Fractals,45 (2012), p. 1192–1200. pdf
  72. D. Li, Y.G. Sinai, Bifurcations of solutions of the 2-dimensional Navier-Stokes system. Essays in mathematics and its applications, p. 241–269, Springer, Heidelberg, 2012. pdf
  73. D. Li, H. Smith, X. Zhang, Global well-posedness and scattering for defocusing energy-critical NLS in the exterior of balls with radial data. Math. Res. Lett. 19 (2012), p. 213–232. pdf
  74. D. Li, X. Zhang, On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d≥2. Sci. China Math. 55 (2012), p. 385–434. pdf
  75. D. Li, Y.G. Sinai, Nonsymmetric bifurcations of solutions of the 2D Navier-Stokes system. Adv. Math. 229 (2012), p.1976–1999. pdf
  76. D. Li, T. Li, Shock formation in a traffic flow model with Arrhenius look-ahead dynamics. Netw. Heterog. Media, 6 (2011), p. 681–694. pdf
  77. D. Li, T. Li, K. Zhao, On a hyperbolic-parabolic system modeling chemotaxis. Math. Models Methods Appl. Sci. 21 (2011), p.1631–1650. pdf
  78. D. Li, X. Zhang, Stability of solutions for nonlinear Schrödinger equations in critical spaces. Sci. China Math. 54 (2011), p. 973–986. pdf
  79. D. Li, J.L. Rodrigo, On a one-dimensional nonlocal flux with fractional dissipation. SIAM J. Math. Anal. 43 (2011), p. 507–526. pdf
  80. D. Li, X. Zhang, Dynamics for the energy critical nonlinear wave equation in high dimensions. Trans. Amer. Math. Soc. 363 (2011), p. 1137–1160. pdf
  81. D. Li, X. Zhang, On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data. Dyn. Partial Differ. Equ. 7 (2010), p. 345–373. pdf
  82. D. Li, X. Zhang, Smoothing estimates of the radial Schrödinger propagator in dimensions n≥2. Acta Math. Sci. Ser. B (Engl. Ed.), 30 (2010), p. 2103–2109. pdf
  83. D. Li, On a class of strongly contractive quadratic recurrence systems. (Russian) Sovrem. Mat. Fundam. Napravl. 36 (2010), p.112–124; translation in J. Math. Sci. (N.Y.), 171 (2010), p. 116–129. pdf
  84. E. Dinaburg, D. Li, Y.G. Sinai, Navier-Stokes system on the unit square with no slip boundary condition. J. Stat. Phys. 141 (2010), p. 342–358. pdf
  85. D. Li, X. Zhang, Global wellposedness and blowup of solutions to a nonlocal evolution problem with singular kernels. Commun. Pure Appl. Anal. 9 (2010), p. 1591–1606. pdf
  86. D. Li, Y.G. Sinai, Blowups of complex-valued solutions for some hydrodynamic models. Regul. Chaotic Dyn. 15 (2010), p. 521–531. pdf
  87. D. Li, J.L. Rodrigo, X. Zhang, Exploding solutions for a nonlocal quadratic evolution problem. Rev. Mat. Iberoam. 26 (2010), p. 295–332. pdf
  88. D. Li, J.L. Rodrigo, Wellposedness and regularity of solutions of an aggregation equation. Rev. Mat. Iberoam. 26 (2010), p.261–294. pdf
  89. D. Li, X. Zhang, Regularity of almost periodic modulo scaling solutions for mass-critical NLS and applications. Anal. PDE 3 (2010), p.175–195. pdf
  90. E. Dinaburg, D. Li, Y.G. Sina, Navier-Stokes system on the flat cylinder and unit square with slip boundary conditions. Commun. Contemp. Math. 12 (2010), p. 325–349. pdf
  91. H. Dong, D. Li, On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces. J. Differential Equations 248 (2010), p. 2684–2702. pdf
  92. D. Li, Y.G. Sinai, Singularities of complex-valued solutions of the two-dimensional Burgers system. J. Math. Phys. 51 (2010), 015205. pdf
  93. J.Y. Cai, X. Chen, D. Li, Quadratic lower bound for permanent vs. determinant in any characteristic. Comput. Complexity, 19 (2010), p. 37–56. pdf
  94. D. Li, X. Zhang, On a nonlocal aggregation model with nonlinear diffusion. Discrete Contin. Dyn. Syst. 27 (2010), p. 301–323. pdf
  95. E. Dinaburg, D. Li, Y.G. Sinai, A new boundary problem for the two dimensional Navier-Stokes system. J. Stat. Phys. 135 (2009), p. 737–750. pdf
  96. D. Li, X. Zhang, On the rigidity of minimal mass solutions to the focusing mass-critical NLS for rough initial data. Electron. J. Differential Equations, (2009), p.1-19. pdf
  97. D. Li, Existence theorems for the 2D quasi-geostrophic equation with plane wave initial conditions. Nonlinearity, 22 (2009), p.1639–1651. pdf
  98. H. Dong, D. Du, D. Li, Finite time singularities and global well-posedness for fractal Burgers equations. Indiana Univ. Math. J. 58 (2009), p. 807–821. pdf
  99. H. Dong, D. Li, Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations. Commun. Math. Sci. 7 (2009), p. 67–80. pdf
  100. R. Killip, D. Li, M. Visan, X. Zhang, Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS. SIAM J. Math. Anal. 41 (2009), p. 219–236. pdf
  101. D. Li, Y.G. Sinai, Asymptotic behavior of generalized convolutions. Regul. Chaotic Dyn. 14 (2009), p. 248–262. pdf
  102. D. Li, X. Zhang, Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions. J. Funct. Anal. 256 (2009), p.1928–1961. pdf
  103. D. Li, On a nonlinear recurrent relation. J. Stat. Phys. 134 (2009), p. 681–700. pdf
  104. D. Li, J.L. Rodrigo, Refined blowup criteria and nonsymmetric blowup of an aggregation equation. Adv. Math. 220 (2009), p. 1717–1738. pdf
  105. D. Li, X. Zhang, On the classification of minimal mass blowup solutions of the focusing mass-critical Hartree equation. Adv. Math. 220 (2009), p. 1171–1192. pdf
  106. D. Li, J. Rodrigo, Finite-time singularities of an aggregation equation in Rn with fractional dissipation. Comm. Math. Phys. 287 (2009), p. 687–703. pdf
  107. D. Li, C. Miao, X. Zhang, The focusing energy-critical Hartree equation. J. Differential Equations, 246 (2009), p. 1139–1163. pdf
  108. W. E, D. Li, On the crystallization of 2D hexagonal lattices. Comm. Math. Phys. 286 (2009), p.1099–1140. pdf
  109. D. Li, J. Rodrigo, Blow up for the generalized surface quasi-geostrophic equation with supercritical dissipation. Comm. Math. Phys.286 (2009), p.111–124. pdf
  110. J.Y. Cai, X. Chen, D. Li, A quadratic lower bound for the permanent and determinant problem over any characteristic ≠2. STOC'08, ACM, New York, 2008, p. 491–497 pdf
  111. D. Li, Y.G. Sinai, Complex singularities of the Burgers system and renormalization group method. Current developments in mathematics, 2006, p.181–210. Int. Press, Somerville, MA, 2008. pdf
  112. D. Li, Y.G. Sinai, Complex singularities of solutions of some 1D hydrodynamic models. Phys. D, 237 (2008), p. 1945–1950. pdf
  113. H. Dong, D. Li, Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations. Arch. Ration. Mech. Anal. 189 (2008), p. 131–158. pdf
  114. D. Li, J. Rodrigo, Blow-up of solutions for a 1D transport equation with nonlocal velocity and supercritical dissipation. Adv. Math. 217 (2008), p. 2563–2568. pdf
  115. H. Dong, D. Li, Finite time singularities for a class of generalized surface quasi-geostrophic equations. Proc. Amer. Math. Soc.136 (2008), p. 2555–2563. pdf
  116. D. Li, Y.G. Sinai, Blow ups of complex solutions of the 3D Navier-Stokes system and renormalization group method. J. Eur. Math. Soc. 10 (2008), p. 267–313. pdf
  117. W. E, D. Li, The Andersen thermostat in molecular dynamics. Comm. Pure Appl. Math. 61 (2008), p. 96–136. pdf
  118. D. Li, On the rate of convergence to equilibrium of the Andersen thermostat in molecular dynamics. J. Stat. Phys. 129 (2007), p. 265–287. pdf
  119. D. Li, F.J. Hickernell, Trigonometric spectral collocation methods on lattices. Recent advances in scientific computing and partial differential equations (Hong Kong, 2002), p.121–132, Contemp. Math., 330, Amer. Math. Soc., Providence, RI, 2003. pdf

Analysis and Partial Differential Equations

  1. D. Li, Global well-posedness of hedgehog solutions for the (3+1) Skyrme model. Duke Math. J. 170 (2021), p.1377–1418. pdf
  2. D. Li, F. Wang, K. Yang, An improved gradient bound for 2D MBE. J. Differential Equations 269(2020), p.11165–11171. pdf
  3. D. Li, J. Rodrigo, Remarks on a nonlocal transport. Adv. Math. 374 (2020), 107345 pdf
  4. D. Li, On some conjectures of Heywood. Pacific J. Math. 306 (2020), p.221–263. pdf
  5. J. Bourgain, D. Li, Galilean boost and non-uniform continuity for incompressible Euler. Comm. Math. Phys. 372 (2019), p.261–280. pdf
  6. T. Hmidi, D. Li, Dynamics of one-fold symmetric patches for the aggregation equation and collapse to singular measure. Anal. PDE 12 (2019), p.2003–2065. pdf
  7. D. Li, X. Zhang, A regularity upgrade of pressure. Contemp. Math., 725 (2019), p. 163–185. pdf
  8. D. Li, On Kato-Ponce and fractional Leibniz. Rev. Mat. Iberoam. 35 (2019), p.23–100. pdf
  9. B. Han, Z. Lei, D. Li, N. Zhao, Sharp one component regularity for Navier-Stokes. Arch. Ration. Mech. Anal. 231 (2019), p. 939–970. pdf
  10. C. Boldrighini, D. Li, Y.G. Sinai, Complex singular solutions of the 3-d Navier-Stokes equations and related real solutions. J. Stat. Phys. 167 (2017), p.1–13. pdf
  11. T. Hmidi, D. Li, Small B∞,∞-1 implies regularity. Dyn. Partial Differ. Equ., 14 (2017), p.1–4. pdf
  12. D. Li, Z. Qiao, T. Tang, Gradient bounds for a thin film epitaxy equation. J. Differential Equations 262 (2017), p.1720–1746. pdf
  13. S. Le Coz, D. Li, T.P. Tsai, Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations. Proc. Roy. Soc. Edinburgh Sect. A, 145 (2015), p.1251–1282. pdf
  14. J. Bourgain, D. Li, Strong illposedness of the incompressible Euler equation in integer Cm spaces. Geom. Funct. Anal. 25 (2015), p.1–86. pdf
  15. H. Dong, D. Li, Global H˙1∩H˙−1 solutions to a logarithmically regularized 2D Euler equation. J. Math. Fluid Mech. 17 (2015), p.1–7. pdf
  16. D. Li, Y. Wu, The Cauchy problem for the two dimensional Euler-Poisson system. J. Eur. Math. Soc. 16 (2014), p. 2211–2266. pdf
  17. D. Li, G. Xu, X. Zhang, On the dispersive estimate for the Dirichlet Schrödinger propagator and applications to energy critical NLS. Canad. J. Math. 66 (2014), p.1110–1142. pdf
  18. Z. Lei, D. Li, X. Zhang, Remarks of global wellposedness of liquid crystal flows and heat flows of harmonic maps in two dimensions. Proc. Amer. Math. Soc. 142 (2014), p. 3801–3810. pdf
  19. D Li, X. Yu, On some Liouville type theorems for the compressible Navier-Stokes equations. Discrete Contin. Dyn. Syst. 34 (2014), p. 4719–4733. pdf
  20. J. Jang, D. Li, X. Zhang, Smooth global solutions for the two-dimensional Euler Poisson system. Forum Math. 26 (2014), p. 645–701. pdf
  21. D. Li, C. Miao, L. Xue, On the well-posedness of a 2D nonlinear and nonlocal system arising from the dislocation dynamics. Commun. Contemp. Math. 16 (2014), 1350021. pdf
  22. H. Dong, D. Li, On a generalized maximum principle for a transport-diffusion model with log-modulated fractional dissipation. Discrete Contin. Dyn. Syst. 34 (2014), p. 3437–3454. pdf
  23. H. Dong, D. Li, On a one-dimensional α-patch model with nonlocal drift and fractional dissipation. Trans. Amer. Math. Soc. 366 (2014), p. 2041–2061. pdf
  24. D. Li, On a frequency localized Bernstein inequality and some generalized Poincaré-type inequalities. Math. Res. Lett. 20 (2013), p.933–945. pdf
  25. D. Li, X. Xu, Global wellposedness of an inviscid 2D Boussinesq system with nonlinear thermal diffusivity. Dyn. Partial Differ. Equ. 10 (2013), p. 255–265. pdf
  26. D. Li, X. Yu, Z. Zhai, On the Euler-Poincaré equation with non-zero dispersion. Arch. Ration. Mech. Anal. 210 (2013), p. 955–974. pdf
  27. D. Li, C. Miao, X. Zhang, On the isentropic compressible Euler equation with adiabatic index γ=1. Pacific J. Math. 262 (2013), p. 109–128. pdf
  28. A. Bulut, M. Czubak, D. Li, N Pavlović, X. Zhang, Stability and unconditional uniqueness of solutions for energy critical wave equations in high dimensions. Comm. Partial Differential Equations, 38 (2013), p. 575–607. pdf
  29. S. Dai, D. Li, K. Zhao, Finite-time quenching of competing species with constrained boundary evaporation. Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), p. 1275–1290. pdf
  30. D. Li, X. Zhang, Wave operators for nonlinear wave equations with null structures. Recent advances in harmonic analysis and partial differential equations, Contemp. Math., 581(2012), p. 257–269. pdf
  31. D. Li, Bifurcation of critical points for solutions of the 2D Euler and 2D quasi-geostrophic equations. J. Stat. Phys. 149 (2012), p. 92–107. pdf
  32. N. Chernov, D. Li, Decay of Fourier modes of solutions to the dissipative surface quasi-geostrophic equations on a finite domain. Chaos Solitons Fractals,45 (2012), p. 1192–1200. pdf
  33. D. Li, H. Smith, X. Zhang, Global well-posedness and scattering for defocusing energy-critical NLS in the exterior of balls with radial data. Math. Res. Lett. 19 (2012), p. 213–232. pdf
  34. D. Li, X. Zhang, On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d≥2. Sci. China Math. 55 (2012), p. 385–434. pdf
  35. D. Li, Y.G. Sinai, Nonsymmetric bifurcations of solutions of the 2D Navier-Stokes system. Adv. Math. 229 (2012), p.1976–1999. pdf
  36. D. Li, T. Li, Shock formation in a traffic flow model with Arrhenius look-ahead dynamics. Netw. Heterog. Media, 6 (2011), p. 681–694. pdf
  37. D. Li, X. Zhang, Stability of solutions for nonlinear Schrödinger equations in critical spaces. Sci. China Math. 54 (2011), p. 973–986. pdf
  38. D. Li, J.L. Rodrigo, On a one-dimensional nonlocal flux with fractional dissipation. SIAM J. Math. Anal. 43 (2011), p. 507–526. pdf
  39. D. Li, X. Zhang, Dynamics for the energy critical nonlinear wave equation in high dimensions. Trans. Amer. Math. Soc. 363 (2011), p. 1137–1160. pdf
  40. D. Li, X. Zhang, On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data. Dyn. Partial Differ. Equ. 7 (2010), p. 345–373. pdf
  41. D. Li, X. Zhang, Smoothing estimates of the radial Schrödinger propagator in dimensions n≥2. Acta Math. Sci. Ser. B (Engl. Ed.), 30 (2010), p. 2103–2109. pdf
  42. E. Dinaburg, D. Li, Y.G. Sinai, Navier-Stokes system on the unit square with no slip boundary condition. J. Stat. Phys. 141 (2010), p. 342–358. pdf
  43. D. Li, X. Zhang, Global wellposedness and blowup of solutions to a nonlocal evolution problem with singular kernels. Commun. Pure Appl. Anal. 9 (2010), p. 1591–1606. pdf
  44. D. Li, Y.G. Sinai, Blowups of complex-valued solutions for some hydrodynamic models. Regul. Chaotic Dyn. 15 (2010), p. 521–531. pdf
  45. D. Li, J.L. Rodrigo, X. Zhang, Exploding solutions for a nonlocal quadratic evolution problem. Rev. Mat. Iberoam. 26 (2010), p. 295–332. pdf
  46. D. Li, J.L. Rodrigo, Wellposedness and regularity of solutions of an aggregation equation. Rev. Mat. Iberoam. 26 (2010), p.261–294. pdf
  47. D. Li, X. Zhang, Regularity of almost periodic modulo scaling solutions for mass-critical NLS and applications. Anal. PDE 3 (2010), p.175–195. pdf
  48. H. Dong, D. Li, On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces. J. Differential Equations 248 (2010), p. 2684–2702. pdf
  49. D. Li, Y.G. Sinai, Singularities of complex-valued solutions of the two-dimensional Burgers system. J. Math. Phys. 51 (2010), 015205. pdf
  50. D. Li, X. Zhang, On a nonlocal aggregation model with nonlinear diffusion. Discrete Contin. Dyn. Syst. 27 (2010), p. 301–323. pdf
  51. E. Dinaburg, D. Li, Y.G. Sinai, A new boundary problem for the two dimensional Navier-Stokes system. J. Stat. Phys. 135 (2009), p. 737–750. pdf
  52. D. Li, X. Zhang, On the rigidity of minimal mass solutions to the focusing mass-critical NLS for rough initial data. Electron. J. Differential Equations, (2009), p.1-19. pdf
  53. D. Li, Existence theorems for the 2D quasi-geostrophic equation with plane wave initial conditions. Nonlinearity, 22 (2009), p.1639–1651. pdf
  54. H. Dong, D. Du, D. Li, Finite time singularities and global well-posedness for fractal Burgers equations. Indiana Univ. Math. J. 58 (2009), p. 807–821. pdf
  55. H. Dong, D. Li, Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations. Commun. Math. Sci. 7 (2009), p. 67–80. pdf
  56. R. Killip, D. Li, M. Visan, X. Zhang, Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS. SIAM J. Math. Anal. 41 (2009), p. 219–236. pdf
  57. D. Li, X. Zhang, Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions. J. Funct. Anal. 256 (2009), p.1928–1961. pdf
  58. D. Li, J.L. Rodrigo, Refined blowup criteria and nonsymmetric blowup of an aggregation equation. Adv. Math. 220 (2009), p. 1717–1738. pdf
  59. D. Li, X. Zhang, On the classification of minimal mass blowup solutions of the focusing mass-critical Hartree equation. Adv. Math. 220 (2009), p. 1171–1192. pdf
  60. D. Li, J. Rodrigo, Finite-time singularities of an aggregation equation in Rn with fractional dissipation. Comm. Math. Phys. 287 (2009), p. 687–703. pdf
  61. D. Li, C. Miao, X. Zhang, The focusing energy-critical Hartree equation. J. Differential Equations, 246 (2009), p. 1139–1163. pdf
  62. D. Li, Y.G. Sinai, Complex singularities of the Burgers system and renormalization group method. Current developments in mathematics, 2006, p.181–210. Int. Press, Somerville, MA, 2008. pdf
  63. H. Dong, D. Li, Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations. Arch. Ration. Mech. Anal. 189 (2008), p. 131–158. pdf
  64. D. Li, J. Rodrigo, Blow-up of solutions for a 1D transport equation with nonlocal velocity and supercritical dissipation. Adv. Math. 217 (2008), p. 2563–2568. pdf
  65. H. Dong, D. Li, Finite time singularities for a class of generalized surface quasi-geostrophic equations. Proc. Amer. Math. Soc.136 (2008), p. 2555–2563. pdf

Fluid Dynamics

Mathematical Physics

Mathematical Biology

  1. L. Guan, D. Li, K. Wang, K. Zhao, On a class of nonlocal SIR models. J. Math. Biol. 78 (2019), p.1581–1604. pdf
  2. D. Li; R. Pan; K. Zhao, Quantitative decay of a one-dimensional hybrid chemotaxis model with large data. Nonlinearity, 28 (2015), p.2181–2210. pdf
  3. D. Li, T. Li, K. Zhao, On a hyperbolic-parabolic system modeling chemotaxis. Math. Models Methods Appl. Sci. 21 (2011), p.1631–1650. pdf

Numerical Analysis

  1. D. Li, C. Quan, W. Yang, The BDF3/EP3 scheme for MBE with no slope selection is stable. J. Sci. Comput, (2021) 89:33. pdf
  2. X. Cheng, D. Li, C. Quan, W. Yang, On a parabolic sine-Gordon model. Numer. Math. Theor. Meth. Appl, 14 (2021), p.1068-1084. pdf
  3. X. Cheng, D. Li, K. Promislow, B. Wetton, Asymptotic behaviour of time stepping methods for phase field models. J. Sci. Comput., 86(2021), p.1-34. pdf
  4. D. Li, Z. Qiao, On second order semi-implicit Fourier spectral methods for 2D Cahn-Hilliard equations. J. Sci. Comput. 70 (2017), p.301–341. pdf
  5. D. Li, Z. Qiao, T. Tang, Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations. SIAM J. Numer. Anal. 54 (2016), p.1653–1681. pdf
  6. D. Li, F. J. Hickernell, Trigonometric spectral collocation methods on lattices. Recent advances in scientific computing and partial differential equations (Hong Kong, 2002), p.121–132, Contemp. Math., 330, Amer. Math. Soc., Providence, RI, 2003. pdf