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



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


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.


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

2010 Mathematics Subject Classification

35Q35, 76D03

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