Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2020; 57(5): 1151-1164

Online first article July 9, 2020      Printed September 30, 2020

https://doi.org/10.4134/BKMS.b190828

Copyright © The Korean Mathematical Society.

Remarks on Liouville type theorems for the 3D stationary MHD equations

Zhouyu Li, Pan Liu, Pengcheng Niu

Northwestern Polytechnical University; Beijing Institute of Technology; Northwestern Polytechnical University

Abstract

The aim of this paper is to establish Liouville type results for the stationary MHD equations. In particular, we show that the velocity and magnetic field, belonging to some Lorentz spaces, must be zero. Moreover, we also obtain Liouville type theorem for the case of axially symmetric MHD equations. Our results generalize previous works by Schulz \cite{Sc2018} and Seregin-Wang \cite{SW2018}.

Keywords: Liouville type theorem, MHD equations, Lorentz space

MSC numbers: 35Q35, 35B65, 76W05

Supported by: This work was financially supported by NSFC 11601423