Communications in Mathematical Sciences

Volume 18 (2020)

Number 3

The local well-posedness to the density-dependent magnetic Bénard system with nonnegative density

Pages: 725 – 750

DOI: https://dx.doi.org/10.4310/CMS.2020.v18.n3.a7

Author

Xin Zhong (School of Mathematics and Statistics, Southwest University, Chongqing, China)

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.

Keywords

density-dependent magnetic Bénard system, strong solutions, Cauchy problem

2010 Mathematics Subject Classification

35Q35, 76D03

Full Text (PDF format)

The author was supported by National Natural Science Foundation of China (No. 11901474).

Received 5 April 2019

Accepted 18 November 2019

Published 30 June 2020