Communications in Mathematical Sciences
Volume 18 (2020)
The local well-posedness to the density-dependent magnetic Bénard system with nonnegative density
Pages: 725 – 750
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
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