THE LOCAL WELL-POSEDNESS TO THE DENSITY-DEPENDENT MAGNETIC BÉNARD SYSTEM WITH NONNEGATIVE DENSITY*

Abstract

We study the Cauchy problem of density-dependent magnetic Bénard system with zero density at infinity on the whole two-dimensional (2D) space. Despite the degenerate nature of the problem, we show the local existence of a unique strong solution in weighted Sobolev spaces by energy method.