Local well-posedness to the 2D Cauchy problem of full compressible magnetohydrodynamic equations with vacuum at infinity

Abstract

This paper concerns the Cauchy problem of two-dimensional (2D) full compressible magnetohydrodynamic (MHD) equations in the whole plane ${\mathbb{R}}^2$ with zero density at infinity. By spatial weighted energy method, we derive the local existence and uniqueness of strong solutions provided that the initial density and the initial magnetic field decay not too slowly at infinity. Note that the initial temperature does not need to decay slowly at infinity. In particular, vacuum states at both the interior domain and the far field are allowed.

30 pages

References in corpus (4)

• Global solutions to the three-dimensional full compressible magnetohydrodynamic flows
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• On Local Strong Solutions to the Cauchy Problem of Two-Dimensional Density-Dependent Magnetohydrodynamic Equations with Vacuum
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Cited by in corpus (1)

• Global well-posedness to the 2D Cauchy problem of nonhomogeneous heat conducting Navier-Stokes and magnetohydrodynamic equations with vacuum at infinity