Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion

Details Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion

2009-01-19

arxiv.org/abs/0901.2908v1

Mathematics

Analysis of PDEs

Scientific paper

Whether or not classical solutions of the 2D incompressible MHD equations without full dissipation and magnetic diffusion can develop finite-time singularities is a difficult issue. A major result of this paper establishes the global regularity of classical solutions for the MHD equations with mixed partial dissipation and magnetic diffusion. In addition, the global existence, conditional regularity and uniqueness of a weak solution is obtained for the 2D MHD equations with only magnetic diffusion.

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