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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) : 1335-1343. 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 and Applied Analysis, 2009, 8 (6) : 1841-1865. 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 and Continuous Dynamical Systems, 2015, 35 (1) : 301-322. 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 and Continuous Dynamical Systems, 2016, 36 (6) : 2945-2967. doi: 10.3934/dcds.2016.36.2945 |
[5] |
Yana Guo, Yan Jia, Bo-Qing Dong. Global stability solution of the 2D MHD equations with mixed partial dissipation. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 885-902. doi: 10.3934/dcds.2021141 |
[6] |
Yong Zeng. Existence and uniqueness of very weak solution of the MHD type system. Discrete and Continuous Dynamical Systems, 2020, 40 (10) : 5617-5638. 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 and Continuous Dynamical Systems - B, 2022, 27 (1) : 487-522. doi: 10.3934/dcdsb.2021052 |
[8] |
Guangwu Wang, Boling Guo. Global weak solution to the quantum Navier-Stokes-Landau-Lifshitz equations with density-dependent viscosity. Discrete and Continuous Dynamical Systems - B, 2019, 24 (11) : 6141-6166. doi: 10.3934/dcdsb.2019133 |
[9] |
Sadek Gala. A new regularity criterion for the 3D MHD equations in $R^3$. Communications on Pure and Applied Analysis, 2012, 11 (3) : 973-980. doi: 10.3934/cpaa.2012.11.973 |
[10] |
Xuanji Jia, Yong Zhou. Regularity criteria for the 3D MHD equations via partial derivatives. Kinetic and Related Models, 2012, 5 (3) : 505-516. 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) : 183-193. doi: 10.3934/era.2020012 |
[12] |
Feng Cheng, Chao-Jiang Xu. On the Gevrey regularity of solutions to the 3D ideal MHD equations. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6485-6506. doi: 10.3934/dcds.2019281 |
[13] |
Wendong Wang, Liqun Zhang. The $C^{\alpha}$ regularity of weak solutions of ultraparabolic equations. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1261-1275. doi: 10.3934/dcds.2011.29.1261 |
[14] |
Fei Chen, Boling Guo, Xiaoping Zhai. Global solution to the 3-D inhomogeneous incompressible MHD system with discontinuous density. Kinetic and Related Models, 2019, 12 (1) : 37-58. doi: 10.3934/krm.2019002 |
[15] |
Hua Zhong, Chunlai Mu, Ke Lin. Global weak solution and boundedness in a three-dimensional competing chemotaxis. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 3875-3898. doi: 10.3934/dcds.2018168 |
[16] |
Nan Chen, Cheng Wang, Steven Wise. Global-in-time Gevrey regularity solution for a class of bistable gradient flows. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 1689-1711. doi: 10.3934/dcdsb.2016018 |
[17] |
Xuanji Jia, Yong Zhou. Regularity criteria for the 3D MHD equations via partial derivatives. II. Kinetic and Related Models, 2014, 7 (2) : 291-304. 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 and Related Models, 2009, 2 (2) : 293-305. 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 Navier-Stokes Cauchy problem. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1283-1294. doi: 10.3934/dcds.2017053 |
[20] |
Jiří Neustupa. A note on local interior regularity of a suitable weak solution to the Navier--Stokes problem. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1391-1400. doi: 10.3934/dcdss.2013.6.1391 |
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