Publications

In Press

  • D. Li and Ya.G. Sinai.
    An application of the renormalization groupmethod to stable limit laws.
    Submitted to J. Stat. Phys., 06/2014 (15 pages) (update: to appear in JSP)
  • J. Bourgain and D. Li.
    Strong illposedness of the incompressible Euler equation in integer Cᵐ spaces.
    Submitted to Geom. Func. Ana, 05/2014 (76 pages) (update: to appear in Geom. Func. Ana)
  • In-Jee Jeong and D. Li.
    A blow-Up result for dyadic models of the Euler equations.
    Submitted to Comm. Math. Phys., 04/2014 (8 pages) (update: to appear in CMP)
  • J. Bourgain and D. Li.
    Strong Ill-posedness of the incompressible Euler equation inborderline Sobolev spaces.
    to appear in Inventiones Mathematicae
  • S. Le Coz, D. Li and T. Tsai.
    Fast-moving finite and infinite trains of solitons fornonlinear Schrödinger equations
    Submitted to Proceedings Aof Roy. Soc. Edin., 2013 (31 pages) (update: to appear )

Refereed publications

  • J. Bourgain and D. Li.
    On an endpoint Kato-Ponce inequality.
    to appear in Diff. Inte. Eqn., 2014, 32 pages.
  • D. Li and Y. Wu.
    The Cauchy problem for the two dimensional Euler-Poisson system.
    to appear in J. Eur. Math. Soc., 2014, 56 pages.
  • M. Avdeeva, D. Li and Ya.G. Sinai.
    New limiting distributions for the Mobius function.
    to appear in Moscow Journal of Combinatorics and Number Theory, 2014, 39 pages.
  • M. Avdeeva, D. Li and Ya.G. Sinai.
    New Erdős-Kac type theorems for signed measures onsquare-free integers.
    J. Stat. Phys. 154 (2014), no. 1--2, 327--333.
  • H. Dong and D. Li.
    On a generalized maximum principle for a transport-diffusionmodel with log-modulated fractional dissipation.
    Disc. Conti. Dyn. Sys. A 34 (2014), no. 9, 3437--3454.
  • D. Li, C. Miao and L. Xue.
    On the well-posedness of a 2D nonlinear and nonlocal system arising from the dislocation dynamics.
    Comm. Cont. Math., Vol. 16, no. 2 (2014) 1350021 (36 pages).
  • H. Dong and D. Li.
    On a one-dimensional α-patch model with nonlocal drift and fractional dissipation.
    Trans. Amer. Math. Soc. 366 (2014), no. 4, 2041--2061.
  • D. Li and X. Yu.
    On some Liouville type theorems for the compressible Navier-Stokes equations
    Disc. Contin. Dyn. Sys. A 34 (2014), no. 11, 15 pages.
  • J. Jang, D. Li and X. Zhang.
    Smooth global solutions for the two dimensional Euler-Poissonsystem.
    Forum Mathematicum. Volume 26 (2014), Issue 3, Pages 645--701.
  • D. Li.
    On a frequency localized Bernstein inequality and some generalized Poincaré-type inequalities.
    Math. Res. Lett. 20 (2013), no. 5, 933--945.
  • D. Li, X. Yu and Z. Zhai.
    On the Euler-Poincaré equation with non-zero dispersion.
    Arch. Ration. Mech. Anal. 210 (2013), no. 3, 955--974.
  • A. Bulut, M. Czubak, D. Li, N. Pavlović and X. Zhang.
    Stability and unconditional uniqueness of solutions for energycritical wave equations in high dimensions.
    Comm. Partial Differential Equations 38 (2013), no. 4, 575--607.
  • H. Dong and D. Li.
    Global Ḣ¹∩Ḣ⁻¹ solutions to a logarithmically regularized 2D Euler equation.
    to appear in J. Math. Fluid Mech. (8 pages)
  • D. Li and X. Xu.
    Global wellposedness of an inviscid 2D Boussinesq system with nonlinear thermal diffusivity
    Dyn. Partial Differ. Equ. 10 (2013), no. 3, 255--265.
  • D. Li, G. Xu and X. Zhang.
    On the Dispersive Estimate for the Dirichlet Schrödinger Propagator and Applications to Energy Critical NLS.
    to appear in Cana. J. Math. (33 pages)
  • Z. Lei, D. Li and X. Zhang.
    Remarks of global wellposedness of liquid crystal flows and heat flows of harmonic maps in two dimensions.
    to appear in Proc. of AMS. (10 pages)
  • S. Dai, D. Li and K. Zhao.
    Finite-time quenching of competing species with constrained boundary evaporation.
    Disc. Conti. Dyn. Sys. 18, no. 5, 1275--1290, 2013.
  • D. Li, C. Miao and X. Zhang.
    On the isentropic compressible euler equation with adiabatic index γ=1.
    Pacific J. Math. 262 (2013), no. 1, 109--128.
  • N. Chernov and D. Li.
    Regularity of solutionsto the dissipative surface quasi-geostrophic equations on a finite domain.
    Chaos Solitons Fractals 45 (2012), no. 9-10, 1192--1200.
  • D. Li and X. Zhang.
    Waveoperators for nonlinear wave equations with null structure.
    Recent advances in harmonic analysis and partial differential equations, 257--269, Contemp. Math., 581, Amer. Math. Soc., Providence, RI, 2012.
  • D. Li, H.F. Smith and X. Zhang.
    Global wellposedness and scattering for the energy-critical NLSoutside an obstacle.
    Math. Res. Lett. 19, no. 1, 213--232, 2012.
  • D. Li and Ya.G. Sinai.
    Bifurcations of solutions of the2-dimensional Navier-Stokes system.
    Essays in mathematics and its applications, 241--269, Springer, Heidelberg, 2012.
  • D. Li.
    Bifurcation of critical points for solutions of the 2D Euler and 2D quasi-geostrophic equations.
    J. Stat. Phys., 149, no. 1, 92--107, 2012.
  • D. Li and Ya.G. Sinai.
    Nonsymmetric bifurcations of solutions of the 2D Navier--Stokessystem.
    Advances in Mathematics, 229, Issue 3, 1976--1999, 2012.
  • D. Li and X. Zhang.
    On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d≥2.
    Sci. China Math., 55, Number 2,385--434, 2012
  • D. Li and T. Li.
    Shock formation in a traffic flow model withArrhenius look-ahead dynamics.
    Netw. Heterog. Media., 6, Number 4, 681--694, 2011.
  • D. Li and X. Zhang.
    Dynamics for the energy critical nonlinearwave equation in high dimensions.
    Trans. Amer. Math. Soc., 363: 1137--1160, 2011.
  • D. Li, T. Li and K. Zhao.
    On ahyperbolic-parabolic system modeling repulsive chemotaxis.
    Math. Models Methods Appl. Sci., 21, issue 8, 1631--1650, 2011.
  • D. Li and X. Zhang.
    Stability of solutions for nonlinear Schrödinger equations incritical spaces.
    Sci. China Math., 54, no. 5, 973--986, 2011.
  • D. Li and J. Rodrigo.
    On a one-dimensional nonlocal flux withfractional dissipation.
    SIAM J. Math. Anal., 43, no. 1, 507--526, 2011.
  • D. Li and X. Zhang.
    On the focusing mass critical problem in six dimensions withsplitting spherically symmetric initial data.
    Dyn. Partial Differ. Equ., 7, no. 4, 345--373, 2010.
  • D. Li and X. Zhang.
    Smoothing estimates of the radial Schrödinger propagator indimensions n≥2.
    Acta Math. Sci. Ser. B Engl. Ed., 30, no. 6, 2103--2109, 2010.
  • D. Li.
    On a class of strongly contractive quadratic recurrence systems.
    (Russian) Sovrem. Mat. Fundam. Napravl., 36: 112--124, 2010.
    translation in J. Math. Sci. (N. Y.), 171, no. 1, 116--129, 2010.
  • D. Li and X. Zhang.
    Regularity of almost periodic modulo scaling solutionsfor mass-critical NLS and applications.
    Analysis & PDE. 3 (2): 175--195, 2010.
  • H. Dong and D. Li.
    On the 2D critical and supercriticaldissipative quasi-geostrophic equation in Besov spaces.
    J. Diff. Eqn., 248, Issue 11, 2684--2702, 2010.
  • E. Dinaburg, D. Li and Ya.G. Sinai.
    Navier-Stokes system on the flat cylinder and unit square withslip boundary conditions.
    Comm. Cont. Math., 12(2): 325--349, 2010.
  • J. Cai, X. Chen and D. Li.
    Quadratic lower bound forpermanent vs. determinant in any characteristic.
    ComputationalComplexity, 19(1): 37--56, 2010.
  • D. Li and J. Rodrigo.
    Wellposedness and regularity of solutions of an aggregation equation.
    Rev. Mat. Iberoam., 26(1): 261--294, 2010.
  • E. Dinaburg, D. Li and Ya.G. Sinai.
    Navier-Stokes system on the unit square with no slipboundary condition.
    J. Stat. Phys., 141, Number 2, 342--358, 2010.
  • D. Li and Ya.G. Sinai.
    Singularities of complex-valued solutions of the twodimensional Burgers system.
    J. Math. Phys., 51, 015205, 2010.
  • D. Li and Ya.G. Sinai.
    Blowups of complex-valued solutions for some hydrodynamic models.
    Regular. Chao. Dyn., 15, Number 4--5, 521--531, 2010.
  • D. Li and X. Zhang.
    Global wellposedness and blowup of solutions to a nonlocalevolution problem with singular kernels.
    Comm. Pure. Appl. Anal., 9(6): 1591--1606, 2010.
  • D. Li, J. Rodrigo and X. Zhang.
    Exploding solutions for a nonlocal quadratic evolution problem.
    Rev. Mat. Iberoam., 26(1): 295--332, 2010.
  • W. E and D. Li.
    On the crystallization of 2D hexagonal lattices.
    Comm. Math. Phys., 286(3): 1099--1140, 2009.
  • D. Li and J. Rodrigo.
    Blow up for the generalized surface quasi-geostrophicequation with supercritical dissipation.
    Comm. Math. Phys., 286(1): 111--124, 2009.
  • D. Li and X. Zhang.
    Dynamics for the energy critical nonlinear Schrödingerequation in high dimensions.
    J. Funct. Anal., 256(6): 1928--1961, 2009.
  • D. Li and J. Rodrigo.
    Refined blowup criteria and nonsymmetric blowup of an aggregation equation.
    Adv. Math., 220(6): 1717--1738, 2009.
  • R. Killip, D. Li, M. Visan and X. Zhang.
    The characterization of minimal-mass blowup solutions to thefocusing mass-critical NLS.
    SIAM J. Math. Anal., 41: 219--236, 2009.
  • D. Li and J. Rodrigo.
    Finite-time singularities of an aggregation equation in ℝⁿ with fractionaldissipation.
    Comm. Math. Phys, 287(2): 687--703, 2009.
  • D. Li.
    Existence theorems for the 2D quasi-geostrophicequation with plane wave initial conditions.
    Nonlinearity, 22: 1639--1651, 2009.
  • H. Dong, D. Du and D. Li.
    finite time singularities and global well-posedness forBurgers' equation with fractional dissipation.
    Indiana. Math. J., 58(2): 807--822, 2009.
  • D. Li and Ya.G. Sinai.
    Asymptotic behavior of generalized convolutions.
    Reg. Chao. Dyn., 14(2): 248--262, 2009.
  • H. Dong and D. Li
    Optimal local smoothing and analyticity rate estimates for thegeneralized Navier-Stokes equations.
    Comm. Math. Sci., 7(1): 67--80, 2009.
  • D. Li.
    On a nonlinear recurrence relation.
    J. of Stat. Phys., 134 (4): 681--700, 2009.
  • D. Li, C. Miao and X. Zhang.
    The focusing energy-critical Hartree equations.
    J. Diff. Eqn., 246, Issue 3, 1139--1163, 2009.
  • E. Dinaburg, D. Li and Ya.G. Sinai.
    A new boundary problem for the two dimensional Navier-Stokessystem.
    J. Stat. Phys., 135(4): 737--750, 2009.
  • D. Li and X. Zhang.
    On the classification of minimal mass blow up solutionsof the focusing mass-critical Hartree equations.
    Adv. Math., 220: 1171--1192, 2009.
  • D. Li and X. Zhang.
    On a nonlocal aggregation model with nonlinear diffusion.
    Discr. Conti. Dyn. Sys., 27 (1): 301--323, 2009.
  • D. Li and X. Zhang.
    On the rigidity of minimal mass solutions to the focusing mass-critical NLS for rough initial data.
    Electron. J. Diff. Eqns., No. 78, 1--19, 2009.
  • H. Dong and D. Li.
    Spatial analyticity of the solutions to the subcriticaldissipative quasi-geostrophic equations.
    Arch. Rat. Mech. Anal., 189, no. 1, 131--158, 2008.
  • D. Li and Ya. G. Sinai.
    Blow ups of complex solutions of the 3D-Navier-Stokes system and renormalizationgroup method.
    Journal of European Mathematical Society, 10, issue 2, 267--313, 2008.
  • W. E and D. Li.
    The Andersen thermostat in molecular dynamics.
    Comm. Pure Appl. Math., 61, issue 1, 96--136, 2008.
  • D. Li and Ya. G. Sinai.
    Complex singularities of solutions of some 1D hydrodynamic models.
    Physica D, 237, Issues 14--17, 1945--1950, 2008.
  • D. Li and J. Rodrigo.
    Blow up of solutions for a 1D transport equation with nonlocal velocity andsupercritical dissipation.
    Adv. Math., 217, issue 6, 2563--2568, 2008.
  • H. Dong and D. Li.
    Finite time singularities for a class ofgeneralized surface quasi-geostrophic equations.
    Proc. of Amer. Math. Soc., 136: 2555--2563, 2008.
  • D. Li.
    On the rate of convergence to equilibrium of the Andersen thermostat in molecular dynamics.
    J. of Stat. Phys., 129, Number 2, 2007.
  • D. Li and F.J. Hickernell.
    Trigonometric spectral collocation methods on lattices.
    Contemporary Mathematics, 330: 121--132, 2003.