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http://dx.doi.org/10.4134/BKMS.b190828

REMARKS ON LIOUVILLE TYPE THEOREMS FOR THE 3D STATIONARY MHD EQUATIONS  

Li, Zhouyu (School of Mathematics and Statistics Northwestern Polytechnical University)
Liu, Pan (School of Mathematics and Statistics Beijing Institute of Technology)
Niu, Pengcheng (School of Mathematics and Statistics Northwestern Polytechnical University)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.5, 2020 , pp. 1151-1164 More about this Journal
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 [14] and Seregin-Wang [18].
Keywords
Liouville type theorem; MHD equations; Lorentz space;
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