Assistant Professor
University of Illinois at Chicago
Email: mdai@uic.edu
Partial Differential Equations, Fluid Dynamics, Complex Fluids.
[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