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Regularity results for weak solutions of the 3D MHD equations
1.  Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, United States 
[1] 
Tomoyuki Suzuki. Regularity criteria in weak spaces in terms of the pressure to the MHD equations. Conference Publications, 2011, 2011 (Special) : 13351343. doi: 10.3934/proc.2011.2011.1335 
[2] 
Ming He, Jianwen Zhang. Global cylindrical solution to the compressible MHD equations in an exterior domain. Communications on Pure & Applied Analysis, 2009, 8 (6) : 18411865. doi: 10.3934/cpaa.2009.8.1841 
[3] 
Quansen Jiu, Jitao Liu. Global regularity for the 3D axisymmetric MHD Equations with horizontal dissipation and vertical magnetic diffusion. Discrete & Continuous Dynamical Systems, 2015, 35 (1) : 301322. doi: 10.3934/dcds.2015.35.301 
[4] 
Fei Chen, Yongsheng Li, Huan Xu. Global solution to the 3D nonhomogeneous incompressible MHD equations with some large initial data. Discrete & Continuous Dynamical Systems, 2016, 36 (6) : 29452967. doi: 10.3934/dcds.2016.36.2945 
[5] 
Yana Guo, Yan Jia, BoQing Dong. Global stability solution of the 2D MHD equations with mixed partial dissipation. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021141 
[6] 
Yong Zeng. Existence and uniqueness of very weak solution of the MHD type system. Discrete & Continuous Dynamical Systems, 2020, 40 (10) : 56175638. doi: 10.3934/dcds.2020240 
[7] 
Kunquan Li, Yaobin Ou. Global wellposedness of vacuum free boundary problem of isentropic compressible magnetohydrodynamic equations with axisymmetry. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021052 
[8] 
Guangwu Wang, Boling Guo. Global weak solution to the quantum NavierStokesLandauLifshitz equations with densitydependent viscosity. Discrete & Continuous Dynamical Systems  B, 2019, 24 (11) : 61416166. doi: 10.3934/dcdsb.2019133 
[9] 
Sadek Gala. A new regularity criterion for the 3D MHD equations in $R^3$. Communications on Pure & Applied Analysis, 2012, 11 (3) : 973980. doi: 10.3934/cpaa.2012.11.973 
[10] 
Xuanji Jia, Yong Zhou. Regularity criteria for the 3D MHD equations via partial derivatives. Kinetic & Related Models, 2012, 5 (3) : 505516. doi: 10.3934/krm.2012.5.505 
[11] 
Ahmad Mohammad Alghamdi, Sadek Gala, Chenyin Qian, Maria Alessandra Ragusa. The anisotropic integrability logarithmic regularity criterion for the 3D MHD equations. Electronic Research Archive, 2020, 28 (1) : 183193. doi: 10.3934/era.2020012 
[12] 
Feng Cheng, ChaoJiang Xu. On the Gevrey regularity of solutions to the 3D ideal MHD equations. Discrete & Continuous Dynamical Systems, 2019, 39 (11) : 64856506. doi: 10.3934/dcds.2019281 
[13] 
Wendong Wang, Liqun Zhang. The $C^{\alpha}$ regularity of weak solutions of ultraparabolic equations. Discrete & Continuous Dynamical Systems, 2011, 29 (3) : 12611275. doi: 10.3934/dcds.2011.29.1261 
[14] 
Fei Chen, Boling Guo, Xiaoping Zhai. Global solution to the 3D inhomogeneous incompressible MHD system with discontinuous density. Kinetic & Related Models, 2019, 12 (1) : 3758. doi: 10.3934/krm.2019002 
[15] 
Hua Zhong, Chunlai Mu, Ke Lin. Global weak solution and boundedness in a threedimensional competing chemotaxis. Discrete & Continuous Dynamical Systems, 2018, 38 (8) : 38753898. doi: 10.3934/dcds.2018168 
[16] 
Nan Chen, Cheng Wang, Steven Wise. Globalintime Gevrey regularity solution for a class of bistable gradient flows. Discrete & Continuous Dynamical Systems  B, 2016, 21 (6) : 16891711. doi: 10.3934/dcdsb.2016018 
[17] 
Xuanji Jia, Yong Zhou. Regularity criteria for the 3D MHD equations via partial derivatives. II. Kinetic & Related Models, 2014, 7 (2) : 291304. doi: 10.3934/krm.2014.7.291 
[18] 
Jishan Fan, Tohru Ozawa. Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray$\alpha$MHD model. Kinetic & Related Models, 2009, 2 (2) : 293305. doi: 10.3934/krm.2009.2.293 
[19] 
Francesca Crispo, Paolo Maremonti. A remark on the partial regularity of a suitable weak solution to the NavierStokes Cauchy problem. Discrete & Continuous Dynamical Systems, 2017, 37 (3) : 12831294. doi: 10.3934/dcds.2017053 
[20] 
Jiří Neustupa. A note on local interior regularity of a suitable weak solution to the NavierStokes problem. Discrete & Continuous Dynamical Systems  S, 2013, 6 (5) : 13911400. doi: 10.3934/dcdss.2013.6.1391 
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