Liouville theorem for MHD system and its applications

Xian-gao Liu; Xiaotao Zhang

doi:10.3934/cpaa.2018111

Article Contents

2018, Volume 17, Issue 6: 2329-2350. Doi: 10.3934/cpaa.2018111

This issue Previous Article Extremal functions of Moser-Trudinger inequality involving Finsler-Laplacian Next Article The spectral expansion approach to index transforms and connections with the theory of diffusion processes

Liouville theorem for MHD system and its applications

Xian-gao Liu and
Xiaotao Zhang

School of Mathematic Sciences, Fudan University, Shanghai, China

Received: May 31, 2017

Revised: January 31, 2018

Published: June 2018

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Abstract

In this paper, we construct Liouville theorem for the MHD system and apply it to study the potential singularities of its weak solution. And we mainly study weak axi-symmetric solutions of MHD system in $\mathbb{R}^3× (0, T)$.

Keywords:

Incompressible magnetohydrodynamics(MHD),
Liouville theorem,
singularties.

Mathematics Subject Classification: 35Q35, 76W05, 35B65.

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