Global low-energy weak solutions of the equations of three-dimensional compressible magnetohydrodynamics

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33 Citations (Scopus)

Abstract

We prove the global-in-time existence of weak solutions of the equations of compressible magnetohydrodynamics in three space dimensions with initial data small in L² and initial density positive and essentially bounded. A great deal of information concerning partial regularity is obtained: velocity, vorticity, and magnetic field become relatively smooth in positive time (H¹ but not H²) and singularities in the pressure cancel those in a certain multiple of the divergence of the velocity, thus giving concrete expression to conclusions obtained formally from the Rankine–Hugoniot conditions. Copyright © 2012 Springer-Verlag.
Original languageEnglish
Pages (from-to)27-58
JournalArchive for Rational Mechanics and Analysis
Volume205
Issue number1
DOIs
Publication statusPublished - Jul 2012

Citation

Suen, A., & Hoff, D. (2012). Global low-energy weak solutions of the equations of three-dimensional compressible magnetohydrodynamics. Archive for Rational Mechanics and Analysis, 205(1), 27-58. doi: 10.1007/s00205-012-0498-3

Keywords

  • Initial data
  • Weak solution
  • Global existence
  • Smooth solution
  • Stokes system

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