Professor
University of Illinois at Chicago
Email: mdai@uic.edu
On leave for 2022-2023
Princeton University, 2022-2023.
University of Oxford, Fall, 2022.
Institute for Advanced Study, Princeton, 2021-2023.
Partial Differential Equations, Fluid Dynamics, Complex Fluids.
NSF DMS, von Neumann Fellowship of the Institute for Advanced Study, AMS Centennial Fellowship (press release)
Ladyzhenskaya Lecturer, Leipzig, 2022.
AMS Centennial Fellowship, American Mathematical Society, 2022-2023.
von Neumann Fellow, Institute for Advanced Study, Princeton, 2021-2022.
[41]. M. Dai. Reduced models for electron magnetohydrodynamics: well-posedness and singularity formation. arXiv: 2204.01951, 2022. PDF
[40]. M. Dai. Almost sure well-posedness for Hall MHD. arXiv: 2202.04265, 2022. PDF
[39]. M. Dai. Almost sure existence of global weak solutions for supercritical electron MHD. arXiv: 2201.08161, 2022. PDF
[38]. A. Cheskidov and M. Dai. The number of degrees of freedom for the 2D Navier-Stokes equation: a connection with Kraichnan's theory of turbulence. arXiv: 2112.11606, 2021. PDF
[37]. M. Dai and S. Friedlander. Uniqueness and non-uniqueness results for dyadic MHD models. arXiv: 2107.04073, 2021. PDF
[36]. M. Dai, M. Hoeller, Q. Peng and X. Zhang. Kolmogorov's dissipation number and determining wavenumber for dyadic models. arXiv: 2108.12913, 2021. PDF
[35]. M. Dai, B. Vyas and X. Zhang. 1D model for the 3D magnetohydrodynamics. arXiv: 2107.02920, 2021. PDF
[34]. M. Dai. Blow-up of dyadic MHD models with forward energy cascade. arXiv: 2102.03498, 2021. PDF
[33]. M. Dai and H. Liu. Anomalous dissipation of energy and magnetic helicity for the electron-MHD system. arXiv: 1911.03953, 2019. PDF
[32]. M. Dai and S. Friedlander. Dyadic models for ideal MHD. Journal of Mathematical Fluid Mechanics, doi.org/10.1007/s00021-021-00640-9, 2022.
[31]. M. Dai. Blow-up of a dyadic model with intermittency dependence for the Hall MHD. Physica D: Nonlinear Phenomena, doi.org/10.1016/j.physd.2021.133066, 2021.
[30]. M. Dai. Phenomenologies of intermittent Hall MHD turbulence. DCDS-Series B, doi.org/10.3934/dcdsb.2021285, 2022.
[29]. M. Dai and H. Liu. On well-posedness of generalized Hall-magnetohydrodynamics. Zeitschrift fur angewandte Mathematik und Physik, to appear, 2021.
[28]. M. Dai, J. Krol and H. Liu. On uniqueness and helicity conservation of weak solutions to the electron-MHD system. Journal of Mathematical Fluid Mechanics, Vol. 24: 69, 2022.
[27]. M. Dai. Non-uniqueness of weak solutions in Leray-Hopf space for the 3D Hall-MHD system. SIAM Journal of Mathematical Analysis, Vol. 53 (5): 5979—6016, 2021.
[26]. M. Dai. Local well-posedness for the Hall-MHD system in optimal Sobolev spaces. Journal of Differential Equations, Vol. 289: 159—181, 2021.
[25]. M. Dai and H. Liu. Low modes regularity criterion for a chemotaxis-Navier-Stokes system. Communications on Pure and Applied Analysis, Vol. 19 (5): 2713—2735, 2020.
[24]. M. Dai and H. Liu. Application of harmonic analysis techniques to regularity problems of dissipative equations. Contemporary Mathematics, Vol. 748: 35—56, 2020.
[23]. M. Dai. Local well-posedness of the Hall-MHD system in $H^s(\mathbb R^n)$ with $s>\frac n2$. Mathematische Nachrichten, Vol. 293 (1): 67—78, 2020.
[22]. M. Dai and H. Liu. Long time behavior of solutions to the 3D Hall-magneto-hydrodynamics system with one diffusion. Journal of Differential Equations, Vol. 266: 7658—7677, 2019.
[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, Vol. 49 (6): 5007—5030, 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, Section A, Vol. 149 (2): 429—446, 2019. PDF
[18]. A. Cheskidov and M. Dai. On the determining wavenumber for the nonautonomous subcritical SQG equation. Journal of Dynamics and Differential Equations, Vol. 32: 1511—1525, 2020.
[17]. A. Cheskidov and M. Dai. Discontinuity of weak solutions to the 3D NSE and MHD equations in critical and supercritical spaces. Journal of Mathematical Analysis and Applications, Vol. 481(2), 123493, 2020.
[16]. A. Cheskidov and M. Dai. Regularity criteria for the 3D Navier-Stokes and MHD equations. Proceedings of the Edinburgh Mathematical Society, 2020.
[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. Physica D: Nonlinear Phenomena, Vol. 374-375: 1–9, 2018.
[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. Physica D: Nonlinear Phenomena, Vol. 376-377: 204–215, 2018.
[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