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arXiv · 1405.0274

Global Existence for Two Dimensional Compressible Magnetohydrodynamic Flows with Zero Magnetic Diffusivity

Xianpeng Hu
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Abstract

The existence of global-in-time classical solutions to the Cauchy problem of compressible magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linear structure is a degenerated hyperbolic-parabolic system. The solution is constructed as a small perturbation of a constant background in critical spaces. The deformation gradient is introduced to decouple the subtle coupling between the flow and the magnetic field. The $L^1$ dissipation for the velocity is obtained, and the $L^2$ dissipations for the density and the magnetic field are also achieved.

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Xianpeng Hu. 2014-05-01. Global Existence for Two Dimensional Compressible Magnetohydrodynamic Flows with Zero Magnetic Diffusivity. https://arxiv.org/abs/1405.0274

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