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A symmetrization of the relativistic Euler equations with several spatial variables
Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray-$\alpha$-MHD model
1. | Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, China |
2. | Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan |
[1] |
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 |
[2] |
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 |
[3] |
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 |
[4] |
Xiaoping Zhai, Yongsheng Li, Wei Yan. Global well-posedness for the 3-D incompressible MHD equations in the critical Besov spaces. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1865-1884. doi: 10.3934/cpaa.2015.14.1865 |
[5] |
Shihu Li, Wei Liu, Yingchao Xie. Large deviations for stochastic 3D Leray-$ \alpha $ model with fractional dissipation. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2491-2509. doi: 10.3934/cpaa.2019113 |
[6] |
Vladimir V. Chepyzhov, E. S. Titi, Mark I. Vishik. On the convergence of solutions of the Leray-$\alpha $ model to the trajectory attractor of the 3D Navier-Stokes system. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 481-500. doi: 10.3934/dcds.2007.17.481 |
[7] |
Daoyuan Fang, Chenyin Qian. Regularity criterion for 3D Navier-Stokes equations in Besov spaces. Communications on Pure and Applied Analysis, 2014, 13 (2) : 585-603. doi: 10.3934/cpaa.2014.13.585 |
[8] |
Ming Lu, Yi Du, Zheng-An Yao, Zujin Zhang. A blow-up criterion for the 3D compressible MHD equations. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1167-1183. doi: 10.3934/cpaa.2012.11.1167 |
[9] |
Aseel Farhat, M. S Jolly, Evelyn Lunasin. Bounds on energy and enstrophy for the 3D Navier-Stokes-$\alpha$ and Leray-$\alpha$ models. Communications on Pure and Applied Analysis, 2014, 13 (5) : 2127-2140. doi: 10.3934/cpaa.2014.13.2127 |
[10] |
Houyu Jia, Xiaofeng Liu. Local existence and blowup criterion of the Lagrangian averaged Euler equations in Besov spaces. Communications on Pure and Applied Analysis, 2008, 7 (4) : 845-852. doi: 10.3934/cpaa.2008.7.845 |
[11] |
Jishan Fan, Tohru Ozawa. A regularity criterion for 3D density-dependent MHD system with zero viscosity. Conference Publications, 2015, 2015 (special) : 395-399. doi: 10.3934/proc.2015.0395 |
[12] |
Jiahong Wu. Regularity results for weak solutions of the 3D MHD equations. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 543-556. doi: 10.3934/dcds.2004.10.543 |
[13] |
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 |
[14] |
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 |
[15] |
Jishan Fan, Tohru Ozawa. Global Cauchy problem of an ideal density-dependent MHD-$\alpha$ model. Conference Publications, 2011, 2011 (Special) : 400-409. doi: 10.3934/proc.2011.2011.400 |
[16] |
Jitao Liu. On the initial boundary value problem for certain 2D MHD-$\alpha$ equations without velocity viscosity. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1179-1191. doi: 10.3934/cpaa.2016.15.1179 |
[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] |
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 |
[19] |
Wei-Xi Li, Rui Xu. Well-posedness in Sobolev spaces of the two-dimensional MHD boundary layer equations without viscosity. Electronic Research Archive, 2021, 29 (6) : 4243-4255. doi: 10.3934/era.2021082 |
[20] |
Yong Zhou. Remarks on regularities for the 3D MHD equations. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 881-886. doi: 10.3934/dcds.2005.12.881 |
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