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
JournalJournal of Differential Equations
Early online dateSep 2019
DOIs
Publication statusE-pub ahead of print - Sep 2019

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Magnetohydrodynamic Equations
Magnetohydrodynamics
Weak Solution
Existence and Uniqueness
Energy
Navier Stokes equations
Compressible Navier-Stokes Equations
Existence of Weak Solutions
Continuous Dependence
Magnetic fields
Codimension
Discontinuity
Uniqueness
Regularity
Magnetic Field
Gradient
Norm
Three-dimensional
Generalise

Citation

Suen, A. (2019). Existence and uniqueness of low-energy weak solutions to the compressible 3D magnetohydrodynamics equations. Journal of Differential Equations. Advance online publication. doi: 10.1016/j.jde.2019.09.037

Keywords

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