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.
Zhouyu Li, Pan Liu, Pengcheng Niu
Northwestern Polytechnical University; Beijing Institute of Technology; Northwestern Polytechnical University
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
2019; 56(5): 1327-1340
2007; 44(4): 701-708
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