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- D. Li, Global well-posedness of hedgehog solutions for the (3+1) Skyrme model.
*Duke Math. J.*170 (2021), p.1377–1418.**pdf** - 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.** - 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** - D. Li, Effective maximum principles for spectral methods.
*Ann. Appl. Math.,*37 (2021), p. 131–290.**pdf** - 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**) - D. Li, J. Rodrigo, Remarks on a nonlocal transport.
*Adv. Math.*374 (2020), 107345**pdf** - J. Bourgain, D. Li, Galilean boost and non-uniform continuity for incompressible Euler.
*Comm. Math. Phys.*372 (2019), p.261–280.**pdf** - D. Li, On Kato-Ponce and fractional Leibniz.
*Rev. Mat. Iberoam.*35 (2019), p.23–100.**pdf** - 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** - 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** - J. Bourgain, D. Li, Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces.
*Invent. Math.*201 (2015), p. 97–157.**pdf** - J. Bourgain, D. Li, Strong illposedness of the incompressible Euler equation in integer Cm spaces.
*Geom. Funct. Anal.*25 (2015), p.1–86.**pdf** - D. Li, Y. Wu, The Cauchy problem for the two dimensional Euler-Poisson system.
*J. Eur. Math. Soc.*16 (2014), p. 2211–2266.**pdf** - 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** - D. Li, Y.G. Sinai, Nonsymmetric bifurcations of solutions of the 2D Navier-Stokes system.
*Adv. Math.*229 (2012), p.1976–1999.**pdf** - D. Li, J.L. Rodrigo, X. Zhang, Exploding solutions for a nonlocal quadratic evolution problem.
*Rev. Mat. Iberoam.*26 (2010), p. 295–332.**pdf** - D. Li, J.L. Rodrigo, Wellposedness and regularity of solutions of an aggregation equation.
*Rev. Mat. Iberoam.*26 (2010), p.261–294.**pdf** - D. Li, J.L. Rodrigo, Refined blowup criteria and nonsymmetric blowup of an aggregation equation.
*Adv. Math.*220 (2009), p. 1717–1738.**pdf** - 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** - W. E, D. Li, On the crystallization of 2D hexagonal lattices.
*Comm. Math. Phys.*286 (2009), p.1099–1140.**pdf** - 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** - W. E, D. Li, The Andersen thermostat in molecular dynamics.
*Comm. Pure Appl. Math.*61 (2008), p. 96–136.**pdf**

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

- D. Li, Why large time-stepping methods for the Cahn-Hilliard equation is stable.
*(to appear in Math. Comp.)*, (2022)**pdf** - D. Li, C. Quan, J. Xu, Energy-dissipation for time-fractional phase-field equations.
*(to appear in Commun. Pure Appl. Anal.)*, (2022)**pdf** - 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** - 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** - 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** - 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.** - 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** - 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** - 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** - 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** - 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** - 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** - D. Li, C. Quan, The operator-splitting method for Cahn-Hilliard is stable.
*J. Sci. Comput.*, (2022) 90(1): 1-12.**pdf** - D. Li, On fractional smoothness of modulus of functions.
*Ann. Appl. Math.*, 37 (2021), no. 3, p. 394–404.**pdf** - 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** - 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** - 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** - 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** - 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** - 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** - 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** - D. Li, Effective maximum principles for spectral methods.
*Ann. Appl. Math.,*37 (2021), p. 131–290.**pdf** - D. Li, Global well-posedness of hedgehog solutions for the (3+1) Skyrme model.
*Duke Math. J.*170 (2021), p.1377–1418.**pdf** - 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** - 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** - 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** - 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** - D. Li, F. Wang, K. Yang, An improved gradient bound for 2D MBE.
*J. Differential Equations*269(2020), p.11165–11171.**pdf** - D. Li, J. Rodrigo, Remarks on a nonlocal transport.
*Adv. Math.*374 (2020), 107345.**pdf** - D. Li, On some conjectures of Heywood.
*Pacific J. Math.*306 (2020), p.221–263.**pdf** - D. Li, X. Zhang, A regularity upgrade of pressure.
*Contemp. Math.*, 725 (2019), p. 163–185.**pdf** - J. Bourgain, D. Li, Galilean boost and non-uniform continuity for incompressible Euler.
*Comm. Math. Phys.*372 (2019), p.261–280.**pdf** - 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** - D. Li, K. Wang, Symmetric radial decreasing rearrangement can increase the fractional Gagliardo norm in domains.
*Commun. Contemp. Math.*21 (2019), 1850059.**pdf** - L. Guan, D. Li, K. Wang, K. Zhao, On a class of nonlocal SIR models.
*J. Math. Biol.*78 (2019), p.1581–1604.**pdf** - D. Li, On Kato-Ponce and fractional Leibniz.
*Rev. Mat. Iberoam.*35 (2019), p.23–100.**pdf** - 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** - 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** - 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** - 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** - T. Hmidi, D. Li, Small B
_{∞,∞}^{-1}implies regularity.*Dyn. Partial Differ. Equ.*14 (2017), p.1–4.**pdf** - 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** - D. Li, Z. Qiao, T. Tang, Gradient bounds for a thin film epitaxy equation.
*J. Differential Equations*262 (2017), p.1720–1746.**pdf** - 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** - 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** - 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** - J. Bourgain, D. Li, Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces.
*Invent. Math.*201 (2015), p. 97–157.**pdf** - 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** - J. Bourgain, D. Li, Strong illposedness of the incompressible Euler equation in integer Cm spaces.
*Geom. Funct. Anal.*25 (2015), p.1–86.**pdf** - 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** - 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** - D. Li, Y. Wu, The Cauchy problem for the two dimensional Euler-Poisson system.
*J. Eur. Math. Soc.*16 (2014), p. 2211–2266.**pdf** - 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** - J. Bourgain, D. Li, On an endpoint Kato-Ponce inequality.
*Differential Integral Equations,*27 (2014), p. 1037–1072.**pdf** - 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** - 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** - 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** - J. Jang, D. Li, X. Zhang, Smooth global solutions for the two-dimensional Euler Poisson system.
*Forum Math.*26 (2014), p. 645–701.**pdf** - 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** - 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** - 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** - 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** - D. Li, On a frequency localized Bernstein inequality and some generalized Poincaré-type inequalities.
*Math. Res. Lett.*20 (2013), p.933–945.**pdf** - 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** - 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** - 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** - 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** - 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** - 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** - 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** - 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** - 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** - 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** - 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** - D. Li, Y.G. Sinai, Nonsymmetric bifurcations of solutions of the 2D Navier-Stokes system.
*Adv. Math.*229 (2012), p.1976–1999.**pdf** - 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** - D. Li, T. Li, K. Zhao, On a hyperbolic-parabolic system modeling chemotaxis.
*Math. Models Methods Appl. Sci.*21 (2011), p.1631–1650.**pdf** - D. Li, X. Zhang, Stability of solutions for nonlinear Schrödinger equations in critical spaces.
*Sci. China Math.*54 (2011), p. 973–986.**pdf** - D. Li, J.L. Rodrigo, On a one-dimensional nonlocal flux with fractional dissipation.
*SIAM J. Math. Anal.*43 (2011), p. 507–526.**pdf** - 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** - 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** - 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** - 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** - 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** - 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** - D. Li, Y.G. Sinai, Blowups of complex-valued solutions for some hydrodynamic models.
*Regul. Chaotic Dyn.*15 (2010), p. 521–531.**pdf** - D. Li, J.L. Rodrigo, X. Zhang, Exploding solutions for a nonlocal quadratic evolution problem.
*Rev. Mat. Iberoam.*26 (2010), p. 295–332.**pdf** - D. Li, J.L. Rodrigo, Wellposedness and regularity of solutions of an aggregation equation.
*Rev. Mat. Iberoam.*26 (2010), p.261–294.**pdf** - 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** - 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** - 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** - D. Li, Y.G. Sinai, Singularities of complex-valued solutions of the two-dimensional Burgers system.
*J. Math. Phys.*51 (2010), 015205.**pdf** - 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** - D. Li, X. Zhang, On a nonlocal aggregation model with nonlinear diffusion.
*Discrete Contin. Dyn. Syst.*27 (2010), p. 301–323.**pdf** - 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** - 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** - D. Li, Existence theorems for the 2D quasi-geostrophic equation with plane wave initial conditions.
*Nonlinearity,*22 (2009), p.1639–1651.**pdf** - 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** - 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** - 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** - D. Li, Y.G. Sinai, Asymptotic behavior of generalized convolutions.
*Regul. Chaotic Dyn.*14 (2009), p. 248–262.**pdf** - D. Li, X. Zhang, Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions.
*J. Funct. Anal.*256 (2009), p.1928–1961.**pdf** - D. Li, On a nonlinear recurrent relation.
*J. Stat. Phys.*134 (2009), p. 681–700.**pdf** - D. Li, J.L. Rodrigo, Refined blowup criteria and nonsymmetric blowup of an aggregation equation.
*Adv. Math.*220 (2009), p. 1717–1738.**pdf** - 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** - 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** - D. Li, C. Miao, X. Zhang, The focusing energy-critical Hartree equation.
*J. Differential Equations,*246 (2009), p. 1139–1163.**pdf** - W. E, D. Li, On the crystallization of 2D hexagonal lattices.
*Comm. Math. Phys.*286 (2009), p.1099–1140.**pdf** - 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** - 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** - 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** - D. Li, Y.G. Sinai, Complex singularities of solutions of some 1D hydrodynamic models.
*Phys. D,*237 (2008), p. 1945–1950.**pdf** - 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** - 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** - 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** - 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** - W. E, D. Li, The Andersen thermostat in molecular dynamics.
*Comm. Pure Appl. Math.*61 (2008), p. 96–136.**pdf** - 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** - 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**

- D. Li, Global well-posedness of hedgehog solutions for the (3+1) Skyrme model.
*Duke Math. J.*170 (2021), p.1377–1418.**pdf** - D. Li, F. Wang, K. Yang, An improved gradient bound for 2D MBE.
*J. Differential Equations*269(2020), p.11165–11171.**pdf** - D. Li, J. Rodrigo, Remarks on a nonlocal transport.
*Adv. Math.*374 (2020), 107345**pdf** - D. Li, On some conjectures of Heywood.
*Pacific J. Math.*306 (2020), p.221–263.**pdf** - J. Bourgain, D. Li, Galilean boost and non-uniform continuity for incompressible Euler.
*Comm. Math. Phys.*372 (2019), p.261–280.**pdf** - 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** - D. Li, X. Zhang, A regularity upgrade of pressure.
*Contemp. Math.*, 725 (2019), p. 163–185.**pdf** - D. Li, On Kato-Ponce and fractional Leibniz.
*Rev. Mat. Iberoam.*35 (2019), p.23–100.**pdf** - 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** - 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** - T. Hmidi, D. Li, Small B
_{∞,∞}^{-1}implies regularity.*Dyn. Partial Differ. Equ.,*14 (2017), p.1–4.**pdf** - D. Li, Z. Qiao, T. Tang, Gradient bounds for a thin film epitaxy equation.
*J. Differential Equations*262 (2017), p.1720–1746.**pdf** - 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** - J. Bourgain, D. Li, Strong illposedness of the incompressible Euler equation in integer C
^{m}spaces.*Geom. Funct. Anal.*25 (2015), p.1–86.**pdf** - 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** - D. Li, Y. Wu, The Cauchy problem for the two dimensional Euler-Poisson system.
*J. Eur. Math. Soc.*16 (2014), p. 2211–2266.**pdf** - 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** - 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** - 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** - J. Jang, D. Li, X. Zhang, Smooth global solutions for the two-dimensional Euler Poisson system.
*Forum Math.*26 (2014), p. 645–701.**pdf** - 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** - 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** - 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** - D. Li, On a frequency localized Bernstein inequality and some generalized Poincaré-type inequalities.
*Math. Res. Lett.*20 (2013), p.933–945.**pdf** - 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** - 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** - 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** - 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** - 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** - 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** - 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** - 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** - 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** - 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** - D. Li, Y.G. Sinai, Nonsymmetric bifurcations of solutions of the 2D Navier-Stokes system.
*Adv. Math.*229 (2012), p.1976–1999.**pdf** - 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** - D. Li, X. Zhang, Stability of solutions for nonlinear Schrödinger equations in critical spaces.
*Sci. China Math.*54 (2011), p. 973–986.**pdf** - D. Li, J.L. Rodrigo, On a one-dimensional nonlocal flux with fractional dissipation.
*SIAM J. Math. Anal.*43 (2011), p. 507–526.**pdf** - 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** - 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** - 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** - 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** - 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** - D. Li, Y.G. Sinai, Blowups of complex-valued solutions for some hydrodynamic models.
*Regul. Chaotic Dyn.*15 (2010), p. 521–531.**pdf** - D. Li, J.L. Rodrigo, X. Zhang, Exploding solutions for a nonlocal quadratic evolution problem.
*Rev. Mat. Iberoam.*26 (2010), p. 295–332.**pdf** - D. Li, J.L. Rodrigo, Wellposedness and regularity of solutions of an aggregation equation.
*Rev. Mat. Iberoam.*26 (2010), p.261–294.**pdf** - 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** - 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** - D. Li, Y.G. Sinai, Singularities of complex-valued solutions of the two-dimensional Burgers system.
*J. Math. Phys.*51 (2010), 015205.**pdf** - D. Li, X. Zhang, On a nonlocal aggregation model with nonlinear diffusion.
*Discrete Contin. Dyn. Syst.*27 (2010), p. 301–323.**pdf** - 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** - 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** - D. Li, Existence theorems for the 2D quasi-geostrophic equation with plane wave initial conditions.
*Nonlinearity,*22 (2009), p.1639–1651.**pdf** - 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** - 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** - 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** - D. Li, X. Zhang, Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions.
*J. Funct. Anal.*256 (2009), p.1928–1961.**pdf** - D. Li, J.L. Rodrigo, Refined blowup criteria and nonsymmetric blowup of an aggregation equation.
*Adv. Math.*220 (2009), p. 1717–1738.**pdf** - 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** - 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** - D. Li, C. Miao, X. Zhang, The focusing energy-critical Hartree equation.
*J. Differential Equations,*246 (2009), p. 1139–1163.**pdf** - 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** - 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** - 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** - 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**

- L. Guan, D. Li, K. Wang, K. Zhao, On a class of nonlocal SIR models.
*J. Math. Biol.*78 (2019), p.1581–1604.**pdf** - 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** - D. Li, T. Li, K. Zhao, On a hyperbolic-parabolic system modeling chemotaxis.
*Math. Models Methods Appl. Sci.*21 (2011), p.1631–1650.**pdf**

- 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** - 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** - 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** - 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** - 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** - 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**