Existence and uniqueness of low-energy weak solutions to the compressible 3D magnetohydrodynamics equations

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Abstract

We prove the existence and uniqueness of weak solutions of the three dimensional compressible magnetohydrodynamics (MHD) equations. We first obtain the existence of weak solutions with small L²-norm which may display codimension-one discontinuities in density, pressure, magnetic field and velocity gradient. The weak solutions we consider here exhibit just enough regularity and structure which allow us to develop uniqueness and continuous dependence theory for the compressible MHD equations. Our results generalise and extend those for the intermediate weak solutions of compressible Navier-Stokes equations. Copyright © 2019 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)2622-2671
JournalJournal of Differential Equations
Volume268
Issue number6
Early online dateSep 2019
DOIs
Publication statusPublished - Mar 2020

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Citation

Suen, A. (2020). Existence and uniqueness of low-energy weak solutions to the compressible 3D magnetohydrodynamics equations. Journal of Differential Equations, 268(6), 2622-2671. doi: 10.1016/j.jde.2019.09.037

Keywords

  • Compressible magnetohydrodynamics
  • Global weak solutions
  • Uniqueness
  • Continuous dependence