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Decay property of regularity-loss type for quasi-linear hyperbolic systems of viscoelasticity
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 |
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Under a Creative Commons license
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. |
| [2] |
B. Desjardins, C. Le Bris, Remarks on a nonhomogeneous model of magnetohydrodynamics, Differential and Integral Equations, 11 (1998), 377-394. |
| [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. |
| [4] |
J. F. Gerbeau, C. Le Bris, Existence of solution for a density-dependent magnetohydrodynamic equation, Adv. Differential Equations, 2 (1997), 427-452. |
| [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. |
| [6] |
J. S. Linshiz, E. S. Titi, Analytical study of certain magnetohydrodynamic-$\alpha$ models, J. Math. Phys., 48 (2007), 065504 (28 pages). |
| [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. |
| [8] |
Y. Zhou, J. Fan, Global Cauchy problem for a regularized Leray-$\alpha$-MHD model with partial viscous terms, preprint, 2009. |
| [9] |
Y. Zhou, J. Fan, A regularity criterion for the density-dependent magnetohydrodynamic equations, Math. Meth. Appl. Sci. 33 (2010), 1350-1355. |
show all references
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. |
| [2] |
B. Desjardins, C. Le Bris, Remarks on a nonhomogeneous model of magnetohydrodynamics, Differential and Integral Equations, 11 (1998), 377-394. |
| [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. |
| [4] |
J. F. Gerbeau, C. Le Bris, Existence of solution for a density-dependent magnetohydrodynamic equation, Adv. Differential Equations, 2 (1997), 427-452. |
| [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. |
| [6] |
J. S. Linshiz, E. S. Titi, Analytical study of certain magnetohydrodynamic-$\alpha$ models, J. Math. Phys., 48 (2007), 065504 (28 pages). |
| [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. |
| [8] |
Y. Zhou, J. Fan, Global Cauchy problem for a regularized Leray-$\alpha$-MHD model with partial viscous terms, preprint, 2009. |
| [9] |
Y. Zhou, J. Fan, A regularity criterion for the density-dependent magnetohydrodynamic equations, Math. Meth. Appl. Sci. 33 (2010), 1350-1355. |
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