Communications in Mathematical Sciences

Volume 19 (2021)

Number 7

Global strong solutions for planar full compressible Hall-MHD equations with large initial data

Pages: 1913 – 1943

DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n7.a7

Authors

Suhua Lai (School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, China; and School of Mathematical Sciences, Xiamen University, Xiamen, China)

Xinying Xu (School of Mathematical Sciences, Xiamen University, Xiamen, China)

Abstract

This paper establishes the global existence of strong solutions for planar compressible, viscous, heat-conductive (i.e., full fluids) Hall-MHD equations with large initial data. The uniform positive lower and upper bounds of the density are achieved by adopting the idea from [S. Jiang, Comm. Math. Phys. 200:181–193, 1999] for the Navier–Stokes equation and Calderón–Zygmund decomposition technique. Based on the bounds of the density and the skew-symmetric nature of the Hall term, we derive our conclusion of Theorem 1.1.

Keywords

Hall-MHD, global strong solutions, large initial data

2010 Mathematics Subject Classification

35D35, 35Q35, 76W05

Full Text (PDF format)

This work was partly supported by the National Science Foundation of China (Grant Nos. 11871407 and 12071390).

Received 16 January 2020

Accepted 7 April 2021

Published 7 September 2021