Global existence and stability of classical solutions for the 2D non-resistive compressible MHD system near equilibrium is shown via pure H^s estimates and a novel pseudo-negative-derivative technique that closes the estimates without extra initial data regularity.
Global Existence for Two Dimensional Compressible Magnetohydrodynamic Flows with Zero Magnetic Diffusivity
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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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Global existence and stability of solutions for the 2D non-resistive compressible MHD system
Global existence and stability of classical solutions for the 2D non-resistive compressible MHD system near equilibrium is shown via pure H^s estimates and a novel pseudo-negative-derivative technique that closes the estimates without extra initial data regularity.