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Lidstone problems
An approximation model for the density-dependent magnetohydrodynamic equations
The global Cauchy problem for an approximation model for the
density-dependent MHD system is studied. The vanishing limit on
$\alpha$ is also discussed.
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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.
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J. F. Gerbeau, C. Le Bris, Existence of solution for a density-dependent magnetohydrodynamic equation, Adv. Differential Equations, 2 (1997), 427-452.
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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.
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Y. Zhou, J. Fan, Global Cauchy problem for a regularized Leray-$\alpha$-MHD model with partial viscous terms, preprint, 2009.
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Y. Zhou, J. Fan, A regularity criterion for the density-dependent magnetohydrodynamic equations, Math. Meth. Appl. Sci. 33 (2010), 1350-1355.