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

2009/01/19 by Cao, Chongsheng, Wu, Jiahong · 2 citations
#35B45 #35B65 #76W05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0901.2908

Abstract

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.

Cited by

• Global well-posedness of the inviscid resistive isentropic compressible MHD system
• Mixed 3D-2D asymptotics for the weak and strong solutions of the rotating magnetohydrodynamic system

Related

• The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion
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• Global regularity for the 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion
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• Local existence and uniqueness of solutions for the 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion