# American Institute of Mathematical Sciences

2013, 2013(special): 207-216. doi: 10.3934/proc.2013.2013.207

## An approximation model for the density-dependent magnetohydrodynamic equations

 1 Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037 2 Department of Applied Physics, Waseda University, Tokyo, 169-8555

Received  July 2012 Published  November 2013

The global Cauchy problem for an approximation model for the density-dependent MHD system is studied. The vanishing limit on $\alpha$ is also discussed.
Citation: Jishan Fan, Tohru Ozawa. An approximation model for the density-dependent magnetohydrodynamic equations. Conference Publications, 2013, 2013 (special) : 207-216. doi: 10.3934/proc.2013.2013.207
##### References:
 [1] H. Abidi, M. Paicu, Global existence for the MHD system in critical spaces, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 447-476.  Google Scholar [2] B. Desjardins, C. Le Bris, Remarks on a nonhomogeneous model of magnetohydrodynamics, Differential and Integral Equations, 11 (1998), 377-394.  Google Scholar [3] J. Fan, T. Ozawa, Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray-$\alpha$-MHD model, Kinetic Related Models 2 (2009), 293-305.  Google Scholar [4] J. F. Gerbeau, C. Le Bris, Existence of solution for a density-dependent magnetohydrodynamic equation, Adv. Differential Equations, 2 (1997), 427-452.  Google Scholar [5] M. Holst, E. Lunasin, G. Tsogtgerel, Analysis of a general family of regularized Navier-Stokes and MHD models, J. of Nonlinear Science, 20 (2010), 523-567.  Google Scholar [6] J. S. Linshiz, E. S. Titi, Analytical study of certain magnetohydrodynamic-$\alpha$ models, J. Math. Phys., 48 (2007), 065504 (28 pages).  Google Scholar [7] Y. Yu, K.Li, Existence of solutions for the MHD-Leray-alpha equations and their relations to the MHD equations, J. Math. Anal. Appl.,329 (2007), 298-326.  Google Scholar [8] Y. Zhou, J. Fan, Global Cauchy problem for a regularized Leray-$\alpha$-MHD model with partial viscous terms, preprint, 2009. Google Scholar [9] Y. Zhou, J. Fan, A regularity criterion for the density-dependent magnetohydrodynamic equations, Math. Meth. Appl. Sci. 33 (2010), 1350-1355.  Google Scholar

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##### References:
 [1] H. Abidi, M. Paicu, Global existence for the MHD system in critical spaces, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 447-476.  Google Scholar [2] B. Desjardins, C. Le Bris, Remarks on a nonhomogeneous model of magnetohydrodynamics, Differential and Integral Equations, 11 (1998), 377-394.  Google Scholar [3] J. Fan, T. Ozawa, Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray-$\alpha$-MHD model, Kinetic Related Models 2 (2009), 293-305.  Google Scholar [4] J. F. Gerbeau, C. Le Bris, Existence of solution for a density-dependent magnetohydrodynamic equation, Adv. Differential Equations, 2 (1997), 427-452.  Google Scholar [5] M. Holst, E. Lunasin, G. Tsogtgerel, Analysis of a general family of regularized Navier-Stokes and MHD models, J. of Nonlinear Science, 20 (2010), 523-567.  Google Scholar [6] J. S. Linshiz, E. S. Titi, Analytical study of certain magnetohydrodynamic-$\alpha$ models, J. Math. Phys., 48 (2007), 065504 (28 pages).  Google Scholar [7] Y. Yu, K.Li, Existence of solutions for the MHD-Leray-alpha equations and their relations to the MHD equations, J. Math. Anal. Appl.,329 (2007), 298-326.  Google Scholar [8] Y. Zhou, J. Fan, Global Cauchy problem for a regularized Leray-$\alpha$-MHD model with partial viscous terms, preprint, 2009. Google Scholar [9] Y. Zhou, J. Fan, A regularity criterion for the density-dependent magnetohydrodynamic equations, Math. Meth. Appl. Sci. 33 (2010), 1350-1355.  Google Scholar
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