Existence of weak solutions to the three-dimensional steady compressible magnetohydrodynamic equations
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The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in ℝ3 for any specific heat ratio γ > 1. The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method of weak convergence. According to the author’s knowledge, it is the first result that treats in three dimensions the existence of weak solutions to the steady compressible MHD equations with Γ > 1.
KeywordsSteady compressible Magnetohydrodynamic equations existence for Γ > 1 weighted estimate viscous flux
MR(2000) Subject Classification35Q60 35J47
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- Lions, P. L.: Mathematical Topics in Fluid Mechanics II, Compressible Models, Clarendon Press, Oxford, 1998Google Scholar