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Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray$\alpha$MHD model
A symmetrization of the relativistic Euler equations with several spatial variables
1.  Laboratoire JacquesLouis Lions, Centre National de la Recherche Scientifique, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris, France 
2.  1726 Iwasaki, Hodogaya, Yokohama 2400015, Japan 
[1] 
Reinhard Racke, Jürgen Saal. Hyperbolic NavierStokes equations I: Local wellposedness. Evolution Equations & Control Theory, 2012, 1 (1) : 195215. doi: 10.3934/eect.2012.1.195 
[2] 
Xumin Gu. Wellposedness of axially symmetric incompressible ideal magnetohydrodynamic equations with vacuum under the noncollinearity condition. Communications on Pure & Applied Analysis, 2019, 18 (2) : 569602. doi: 10.3934/cpaa.2019029 
[3] 
Jishan Fan, Yueling Jia. Local wellposedness of the full compressible NavierStokesMaxwell system with vacuum. Kinetic & Related Models, 2018, 11 (1) : 97106. doi: 10.3934/krm.2018005 
[4] 
Xinwei Yu, Zhichun Zhai. On the Lagrangian averaged Euler equations: local wellposedness and blowup criterion. Communications on Pure & Applied Analysis, 2012, 11 (5) : 18091823. doi: 10.3934/cpaa.2012.11.1809 
[5] 
George Avalos, Roberto Triggiani. Semigroup wellposedness in the energy space of a parabolichyperbolic coupled StokesLamé PDE system of fluidstructure interaction. Discrete & Continuous Dynamical Systems  S, 2009, 2 (3) : 417447. doi: 10.3934/dcdss.2009.2.417 
[6] 
Hung Luong. Local wellposedness for the Zakharov system on the background of a line soliton. Communications on Pure & Applied Analysis, 2018, 17 (6) : 26572682. doi: 10.3934/cpaa.2018126 
[7] 
Yong Zhou, Jishan Fan. Local wellposedness for the ideal incompressible density dependent magnetohydrodynamic equations. Communications on Pure & Applied Analysis, 2010, 9 (3) : 813818. doi: 10.3934/cpaa.2010.9.813 
[8] 
Boris Kolev. Local wellposedness of the EPDiff equation: A survey. Journal of Geometric Mechanics, 2017, 9 (2) : 167189. doi: 10.3934/jgm.2017007 
[9] 
Daniel Coutand, Steve Shkoller. A simple proof of wellposedness for the freesurface incompressible Euler equations. Discrete & Continuous Dynamical Systems  S, 2010, 3 (3) : 429449. doi: 10.3934/dcdss.2010.3.429 
[10] 
Elaine Cozzi, James P. Kelliher. Wellposedness of the 2D Euler equations when velocity grows at infinity. Discrete & Continuous Dynamical Systems  A, 2019, 39 (5) : 23612392. doi: 10.3934/dcds.2019100 
[11] 
Sirui Li, Wei Wang, Pingwen Zhang. Local wellposedness and small Deborah limit of a moleculebased $Q$tensor system. Discrete & Continuous Dynamical Systems  B, 2015, 20 (8) : 26112655. doi: 10.3934/dcdsb.2015.20.2611 
[12] 
Fucai Li, Yanmin Mu, Dehua Wang. Local wellposedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces. Kinetic & Related Models, 2017, 10 (3) : 741784. doi: 10.3934/krm.2017030 
[13] 
Yoshihiro Shibata. Local wellposedness of free surface problems for the NavierStokes equations in a general domain. Discrete & Continuous Dynamical Systems  S, 2016, 9 (1) : 315342. doi: 10.3934/dcdss.2016.9.315 
[14] 
Takeshi Wada. A remark on local wellposedness for nonlinear Schrödinger equations with power nonlinearityan alternative approach. Communications on Pure & Applied Analysis, 2019, 18 (3) : 13591374. doi: 10.3934/cpaa.2019066 
[15] 
Márcio Cavalcante, Chulkwang Kwak. Local wellposedness of the fifthorder KdVtype equations on the halfline. Communications on Pure & Applied Analysis, 2019, 18 (5) : 26072661. doi: 10.3934/cpaa.2019117 
[16] 
Vanessa Barros, Felipe Linares. A remark on the wellposedness of a degenerated Zakharov system. Communications on Pure & Applied Analysis, 2015, 14 (4) : 12591274. doi: 10.3934/cpaa.2015.14.1259 
[17] 
Aissa Guesmia, Nassereddine Tatar. Some wellposedness and stability results for abstract hyperbolic equations with infinite memory and distributed time delay. Communications on Pure & Applied Analysis, 2015, 14 (2) : 457491. doi: 10.3934/cpaa.2015.14.457 
[18] 
Wenming Hu, Huicheng Yin. Wellposedness of low regularity solutions to the second order strictly hyperbolic equations with nonLipschitzian coefficients. Communications on Pure & Applied Analysis, 2019, 18 (4) : 18911919. doi: 10.3934/cpaa.2019088 
[19] 
George Avalos, Pelin G. Geredeli, Justin T. Webster. Semigroup wellposedness of a linearized, compressible fluid with an elastic boundary. Discrete & Continuous Dynamical Systems  B, 2018, 23 (3) : 12671295. doi: 10.3934/dcdsb.2018151 
[20] 
Huahui Li, Zhiqiang Shao. Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for generalized Chaplygin gas. Communications on Pure & Applied Analysis, 2016, 15 (6) : 23732400. doi: 10.3934/cpaa.2016041 
2018 Impact Factor: 1.38
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