REMARKS ON LIOUVILLE TYPE THEOREMS FOR THE 3D STATIONARY MHD EQUATIONS
Bull. Korean Math. Soc.
Published online July 9, 2020
Zhouyu Li, Pan Liu, and Pengcheng Niu
Northwestern Polytechnical University, Northwest 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 and Seregin-Wang.
Keywords : Liouville type theorem; MHD equations; Lorentz space
MSC numbers : 35Q35;35B65;76W05
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