Compactness of weak solutions to the three-dimensional compressible magnetohydrodynamic equations |
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Authors: | Xianpeng Hu Dehua Wang |
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Affiliation: | Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA |
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Abstract: | The compactness of weak solutions to the magnetohydrodynamic equations for the viscous, compressible, heat conducting fluids is considered in both the three-dimensional space R3 and the three-dimensional periodic domains. The viscosities, the heat conductivity as well as the magnetic coefficient are allowed to depend on the density, and may vanish on the vacuum. This paper provides a different idea from [X. Hu, D. Wang, Global solutions to the three-dimensional full compressible magnetohydrodynamic flows, Comm. Math. Phys. (2008), in press] to show the compactness of solutions of viscous, compressible, heat conducting magnetohydrodynamic flows, derives a new entropy identity, and shows that the limit of a sequence of weak solutions is still a weak solution to the compressible magnetohydrodynamic equations. |
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Keywords: | 35Q36 35D05 76W05 |
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