Existence theorems for the Cauchy problem of 2D nonhomogeneous incompressible non-resistive MHD equations with vacuum

2017/07/04 by Chen, Mingtao, Zang, Aibin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.05279

Abstract

In this paper, we investigate the Cauchy problem of the nonhomogeneous incompressible non-resistive MHD on ℝ² with vacuum as far field density and prove that the 2D Cauchy problem has a unique local strong solution provided that the initial density and magnetic field decay not too slow at infinity. Furthermore, if the initial data satisfy some additional regularity and compatibility conditions, the strong solution becomes a classical one.

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