Mimi Dai                                                                               

Assistant Professor

Department of Mathematics

University of Illinois at Chicago

Email: mdai@uic.edu


CV                        Publications



Teaching

    Math 210 Fall 2017         Math 480 Fall 2017

 

Research Interests

    Partial Differential Equations, Fluid Dynamics, Complex Fluids.

Publications

[24].  M. Dai.  Local well-posedness of the Hall-MHD system in $H^s(\mathbb R^n)$ with $s>\frac n2$.  arXiv: 1709.02347, 2017.

[23].  M. Dai.  Local existence for the MHD system in optimal Sobolev space.  arXiv: 1707.07754, 2017.

[22].  M. Dai and H. Liu.  Long time behavior of solutions to the 3D Hall-magneto-hydrodynamics system with one diffusion.  arXiv: 1705.02647, 2017.

[21].  J. Bona and M. Dai.  Norm-inflation results for the BBM equation.  Journal of Mathematical Analysis and Applications, Vol. 446: 879--885, 2017.  PDF

[20].  M. Dai. Regularity problem for the nematic LCD system with Q-tensor in $\mathbb R^3$. SIAM Journal on Mathematical Analysis. To appear, 2017.  PDF

[19].  A. Cheskidov and M. Dai. Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations. Proceedings of the Royal Society of Edinburg. To appear, 2017.  PDF

[18].  A. Cheskidov and M. Dai.  On the determining  wavenumber for the nonautonomous subcritical  SQG equation.  arXiv:1508.07943,  2015.

[17].  A. Cheskidov and M. Dai.  Ill-posedness of the Navier-Stokes and magneto-hydrodynamic systems. arXiv: 1510.05733,  2015.

[16].  A. Cheskidov and M. Dai.  Regularity criteria for the 3D Navier-Stokes and MHD equations.  arXiv:1507.06611,  2015.

[15].  M. Dai,  E. Feireisl, E. Rocca, G. Schimperna, and M. E. Schonbek. Analysis of a diffuse interface model of multispecies tumor growth. Nonlinearity, Vol. 30: 1639--1658, 2017. PDF

[14].  A. Cheskidov, M. Dai, and L. Kavlie. Determining modes for the 3D Navier-Stokes equations.  arXiv:1507.05908,  2015.

[13].  M. Dai.  Regularity criterion for the 3D Hall-magneto-hydrodynamics. Journal of Differential Equations, 261: 573--591, 2016.  PDF

[12].  A. Cheskidov and M. Dai. Determining modes for the surface quasi-geostrophic equation.  arXiv:1507.01075,  2015.

[11].  M. Dai.  Regularity criterion and energy conservation for the supercritical quasi-geostrophic equation.  Journal of Mathematical Fluid Mechanics, DOI:10.1007/s00021-017-0320-y, 2017.  PDF

[10].  M. Dai.  Stability of solutions to the quasi-geostrophic equations in $\mathbb R^2$.  Nonlinearity, 28: 4227--4248, 2015.  PDF

[9].   M. Dai,  E. Feireisl, E. Rocca, G. Schimperna and M. E. Schonbek.  On asymptotic isotropy for a hydrodynamic model of liquid crystals.  Asymptotic Analysis, 97(3-4): 189--210, 2016.  PDF

[8].   A. Cheskidov and M. Dai.  The existence of a global attractor for the forced critical surface quasi-geostrophic equation in $L^2$.  Journal of Mathematical Fluid Mechanics, DOI: 10.1007/s00021-017-0324-7, 2017.  PDF

[7].   M. Dai.  Existence of regular solutions to an Ericksen-Leslie model of liquid crystal system, Communications in Mathematical Sciences, Vol. 13(7): 1711--1740, 2014.  PDF

[6].   A. Cheskidov and M. Dai.  Norm inflation for generalized magneto-hydrodynamic system.  Nonlinearity, Vol. 28: 129--142, 2015.  PDF

[5].   M. Dai and M. E. Schonbek.  Asymptotic behavior of solutions to the liquid crystal systems in$H^m(\mathbb R^3)$.  SIAM Journal on Mathematical Analysis, Vol. 46, No. 5: 3131--3150, 2014.  PDF

[4].   A. Cheskidov and M. Dai.  Norm inflation for generalized Navier-Stokes equations.  Indiana University Mathematics Journal, Vol. 63, No. 3 : 869--884, 2014.  PDF

[3].   M. Dai,  J. Qing,  and M. E. Schonbek.  Asymptotic behavior of solutions to liquid crystal systems in $\mathbb R^3$.   Communications in Partial Differential Equations. Vol. 37, No. 12: 2138--2164, 2012.  PDF

[2].   M. Dai,  J. Qing,  and M. E. Schonbek.   Regularity of solutions to the liquid crystals systems in $\mathbb R^2$ and $\mathbb R^3$.  Nonlinearity, 25: 513--532, 2012.  PDF

[1].   M. Dai,  J. Qing,  and M. E. Schonbek.  Norm inflation for incompressible magneto-hydrodynamic system in $\dot B^{-1,\infty}_{\infty}$.  Advances in Differential Equations, Vol. 16, No. 7-8, 725--746, 2011.  PDF