Mathematical Fluid dynamics

  1. D. Li, Optimal Gevrey regularity for supercritical quasi-geostrophic equations. arXiv:2106.12439.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
  3. 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)
  4. D. Li, J. Rodrigo, Remarks on a nonlocal transport. Adv. Math. 374 (2020), 107345 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. 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
  7. J. Bourgain, D. Li, Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Invent. Math. 201 (2015), p. 97–157. pdf
  8. J. Bourgain, D. Li, Strong illposedness of the incompressible Euler equation in integer Cm spaces. Geom. Funct. Anal. 25 (2015), p.1–86. pdf
  9. D. Li, Y. Wu, The Cauchy problem for the two dimensional Euler-Poisson system. J. Eur. Math. Soc. 16 (2014), p. 2211–2266. pdf
  10. 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
  11. D. Li, Y.G. Sinai, Nonsymmetric bifurcations of solutions of the 2D Navier-Stokes system. Adv. Math. 229 (2012), p.1976–1999. pdf
  12. 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

Dispersive equations and aggregation equations

  1. D. Li, Uniform estimates for 2D quasilinear wave. arXiv:2106.06419.pdf
  2. D. Li, Global well-posedness of hedgehog solutions for the (3+1) Skyrme model. Duke Math. J. 170 (2021), p.1377–1418. pdf
  3. D. Li, Y. Wu, The Cauchy problem for the two dimensional Euler-Poisson system. J. Eur. Math. Soc. 16 (2014), p. 2211–2266. pdf
  4. 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
  5. D. Li, J.L. Rodrigo, X. Zhang, Exploding solutions for a nonlocal quadratic evolution problem. Rev. Mat. Iberoam. 26 (2010), p. 295–332. pdf
  6. D. Li, J.L. Rodrigo, Wellposedness and regularity of solutions of an aggregation equation. Rev. Mat. Iberoam. 26 (2010), p.261–294. pdf
  7. D. Li, X. Zhang, Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions. J. Funct. Anal. 256 (2009), p.1928–1961. pdf
  8. D. Li, J.L. Rodrigo, Refined blowup criteria and nonsymmetric blowup of an aggregation equation. Adv. Math. 220 (2009), p. 1717–1738. pdf
  9. 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

Harmonic analysis

  1. 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.
  2. D. Li, On fractional smoothness of modulus of functions. Ann. Appl. Math., 37 (2021), no. 3, p. 394–404. pdf
  3. D. Li, Effective maximum principles for spectral methods. Ann. Appl. Math., 37 (2021), p. 131–290. pdf
  4. D. Li, On some conjectures of Heywood. Pacific J. Math. 306 (2020), p.221–263. pdf
  5. D. Li, X. Zhang, A regularity upgrade of pressure. Contemp. Math., 725 (2019), p. 163–185. pdf
  6. D. Li, On Kato-Ponce and fractional Leibniz. Rev. Mat. Iberoam. 35 (2019), p.23–100. pdf
  7. T. Hmidi, D. Li, Small B∞,∞-1 implies regularity.Dyn. Partial Differ. Equ. 14 (2017), p.1–4. pdf
  8. J. Bourgain, D. Li, On an endpoint Kato-Ponce inequality. Differential Integral Equations, 27 (2014), p. 1037–1072. pdf
  9. D. Li, On a frequency localized Bernstein inequality and some generalized Poincaré-type inequalities. Math. Res. Lett. 20 (2013), p.933–945. pdf

Numerical analysis and scientific computing

  1. D. Li, Why large time-stepping methods for the Cahn-Hilliard equation is stable. Math. Comp. 91 (2022), no. 338, p. 2501-2515. pdf
  2. J.F Cai, M. Huang, D. Li, Y. Wang, On smoothed amplitude flow models for phase retrieval. pdf
  3. 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
  4. 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
  5. 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
  6. D. Li, C. Quan, The operator-splitting method for Cahn-Hilliard is stable. J. Sci. Comput., (2022) 90(1): 1-12. pdf
  7. 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
  8. 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
  9. D. Li, Effective maximum principles for spectral methods. Ann. Appl. Math., 37 (2021), p. 131–290. 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. W. E, D. Li, On the crystallization of 2D hexagonal lattices. Comm. Math. Phys. 286 (2009), p.1099–1140. pdf
  12. W. E, D. Li, The Andersen thermostat in molecular dynamics. Comm. Pure Appl. Math. 61 (2008), p. 96–136. pdf
  13. 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