Remarks on Liouville type theorems for the 3D stationary MHD equations
Bull. Korean Math. Soc. 2020 Vol. 57, No. 5, 1151-1164
https://doi.org/10.4134/BKMS.b190828
Published online September 30, 2020
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
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