Mimi Dai                                                                               

Research Assistant Professor

Department of Mathematics

University of Illinois at Chicago

Email: mdai@uic.edu

CV                     Research Statement                       Publications

Teaching

Math 210 Fall 2015         Math 480 Fall 2015

 

Research Interests

Partial Differential Equations, Fluid Dynamics, Complex Fluids.

Publications

[18].  KolmogorovŐs dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations (with A. Cheskidov),  arXiv:1510.00379,  2015.

[17].  On the determining  wavenumber for the nonautonomous subcritical  SQG equation (with A. Cheskidov),  arXiv:1508.07943,  2015.

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

[15].  Analysis of a diffuse interface model of multispecies tumor growth (with E. Feireisl, E. Rocca, G. Schimperna, and M. E. Schonbek), 
arXiv:1507.07683,  2015.

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

[13].  Regularity criterion for the 3D Hall-magneto-hydrodynamics, arXiv:1507.05885,  2015.

[12].  Determining modes for the surface quasi-geostrophic equation (with A. Cheskidov), arXiv:1507.01075,  2015.

[11].  Regularity criterion and energy conservation for the supercritical quasi-geostrophic equation,  arXiv:1505.02293,  2015.

[10].  Stability of solutions to the quasi-geostrophic equations in $\mathbb R^2$,  Nonlinearity, Accepted,  arXiv:1503.04742,  2015.

[9].   On asymptotic isotropy for a hydrodynamic model of liquid crystals (with E. Feireisl, E. Rocca, G. Schimperna and M. E. Schonbek),  Asymptotic Analysis, Accepted,  arXiv:1409.7499,  2014.

[8].   The existence of a global attractor for the forced critical surface quasi-geostrophic equation in $L^2$ (with A. Cheskidov),  arXiv:1402.4801,  2014.

[7].   Existence of regular solutions to an Ericksen-Leslie model of liquid crystal system, Communications in Mathematical Sciences. To appear, 2014.arXiv:1309.0476.

[6].   Norm inflation for generalized magneto-hydrodynamic system (with A. Cheskidov), Nonlinearity, Vol. 28: 129--142, 2015. 
arXiv:1402.1897.

[5].   Asymptotic behavior of solutions to the liquid crystal systems in 
$H^m(\mathbb R^3)$ (with M. E. Schonbek), SIAM Journal on Mathematical Analysis, Vol. 46, No. 5: 3131--3150, 2014. 
arXiv:1208.3007.

[4].   Norm inflation for generalized Navier-Stokes equations (with A. Cheskidov), Indiana University Mathematics Journal, Vol. 63, No. 3 : 869--884, 2014. arXiv:1212.3801.

[3].   Asymptotic behavior of solutions to liquid crystal systems in $\mathbb R^3$ (with J. Qing and M. E. Schonbek), Communications in Partial Differential Equations. Vol. 37, No. 12: 2138--2164, 2012. arXiv:1111.1681.

[2].   Regularity of solutions to the liquid crystals systems in $\mathbb R^2$ and $\mathbb R^3$ (with J. Qing and M. E. Schonbek), Nonlinearity, 25: 513--532, 2012.  arXiv:1110.2719.

[1].   Norm inflation for incompressible magneto-hydrodynamic system in $\dot B^{-1,\infty}_{\infty}$ (with J. Qing and M. E. Schonbek), Advances in Differential Equations, Vol. 16, No. 7-8, 725--746, 2011.  arXiv:1110.2472.