Acta Mathematica Sinica, English Series

, Volume 28, Issue 12, pp 2431–2442 | Cite as

Existence of weak solutions to the three-dimensional steady compressible magnetohydrodynamic equations

  • Chun Hui Zhou


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.


Steady compressible Magnetohydrodynamic equations existence for Γ > 1 weighted estimate viscous flux 

MR(2000) Subject Classification

35Q60 35J47 


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Supplementary material

10114_2012_696_MOESM1_ESM.tex (44 kb)
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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjingP. R. China
  2. 2.LCPInstitute of Applied Physics and Computational MathematicsBeijingP. R. China

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