Recent Publications

 A. Cheskidov, M. Dai, and S. Palasek. Instantaneous Type-I blow-up and non-uniqueness of smooth solutions of the Navier-Stokes equations. arXiv:2511.09556, 2025. 

N. Adzic Vukotic M. Dai. Discretely self-similar solutions for electron MHD. arXiv:2510.19000, 2025. 

H. Babaei and M. Dai. Well-posedness of the electron MHD with partial resistivity.  arXiv:2503.18149, 2025.

M. Dai. Blowup for the forced electron MHD. arXiv:2503.14777, 2025.

M. Dai. Well-posedness and blowup of 1D electron magnetohydrodynamics. arXiv:2503.06383, 2025.

M. Dai. Ill-posedness of $2\frac12$D electron MHD.} arXiv:2411.00120, 2024.

M. Dai and S.-J. Oh. Beale--Kato--Majda-type continuation criteria for Hall- and electron-magnetohydrodynamics. arXiv:2407.04314, 2024.

M. Dai. Non-unique solutions for electron MHD. arXiv:2405.14127, 2024. 

M. Dai and Q. Peng. Non-unique weak solutions of forced SQG. arXiv:2310.13537, 2023.

M. Dai. Global existence of 2D electron MHD near a steady state. arXiv:2306.13036, 2023. 

M. Dai, C. Ouyang and Q. Peng. Uniqueness for a stochastic ideal dyadic MHD model.  arXiv:2306.10909, 2023.

M. Dai and Q. Peng. Non-unique stationary solutions of forced SQG. arXiv:2302.03283, 2023.

M. Dai, V. Giri, and R. Radu. An Onsager-type theorem for SQG. arXiv:2407.02582, 2024. 

M. Dai, H. Guerra and C. Wu. Self-similar singularities for electron MHD. Journal of Mathematical Analysis and Applications, Vol. 555, Iss. I, 130029, 2025.

M. Dai. The concept of intermittency dimension in fluid dynamics. Applied Mathematical Modelling, Doi: 10.1016/j.apm.2025.116169, 2025.

M. Dai and C. Wu. Non-unique stationary solutions of even active scalar equations. Evolution Equations and Control Theory, Doi: 10.3934/eect.2025014, 2025.

M. Dai. Reduced models for electron magnetohydrodynamics: well-posedness and singularity formation.  Transactions of AMS, Vol. 378 (6): 3981--4009, 2025.

M. Dai and S. Friedlander. Non-uniqueness of forced active scalar equations with even drift operators. Physica D: Nonlinear Phenomena, Vol. 467, 134271,  https://doi.org/10.1016/j.physd.2024.134271, 2024.

M. Dai, M. Hoeller, Q. Peng and X. Zhang. Kolmogorov's dissipation number and determining wavenumber for dyadic models. Nonlinearity, 37, 025015, https://doi.org/10.1088/1361-6544/ad1af0, 2024.

M. Dai. Almost sure well-posedness for Hall MHD. Journal of Mathematical Fluid Mechanics, Vo. 26, 13, 2024.

M. Dai and C. Wu. Dissipation wavenumber and regularity for electron magnetohydrodynamics.  Journal of Differential Equations, Vol. 376: 655--681, 2023.

M. Dai. Almost sure existence of global weak solutions for supercritical electron MHD. Discrete and Continuous Dynamical Systems Series B, doi:10.3934/dcdsb.2023146, 2023.

M. Dai, B. Vyas and X. Zhang. 1D model for the 3D magnetohydrodynamics.  Journal of Nonlinear Science, doi.org/10.1007/s00332-023-09944-8, 2023.

A. Cheskidov, M. Dai and S. Friedlander. Dyadic models for fluid equations: a survey. Journal of Mathematical Fluid Mechanics, Vol.25, 62, 2023.

M. Dai. Blow-up of dyadic MHD models with forward energy cascade. International Mathematics Research Notices, https://doi.org/10.1093/imrn/rnac337, 2022.

M. Dai and S. Friedlander. Uniqueness and non-uniqueness results for dyadic MHD models.  Journal of Nonlinear Science, https://doi.org/10.1007/s00332-022-09868-9, 2022.

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, 24:69, 2022.

M. Dai. Blow-up of a dyadic model with intermittency dependence for the Hall MHD.  Physica D: Nonlinear Phenomena. DOI: 10.1016/j.physd.2021.133066.

M. Dai. Local well-posedness for the Hall-MHD system in optimal Sobolev spaces. Journal of Differential Equations, Vol. 289: 159--181, 2021.