Well-posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics

Yuri Trakhinin, Tao Wang

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We consider the free boundary problem for non-relativistic and relativistic ideal compressible magnetohydrodynamics in two and three spatial dimensions with the total pressure vanishing on the plasma–vacuum interface. We establish the local-in-time existence and uniqueness of solutions to this nonlinear characteristic hyperbolic problem under the Rayleigh–Taylor sign condition on the total pressure. The proof is based on certain tame estimates in anisotropic Sobolev spaces for the linearized problem and a modification of the Nash–Moser iteration scheme. Our result is uniform in the speed of light and appears to be the first well-posedness result for the free boundary problem in ideal compressible magnetohydrodynamics with zero total pressure on the moving boundary.

Original languageEnglish
Pages (from-to)1131-1176
Number of pages46
JournalArchive for Rational Mechanics and Analysis
Volume239
Issue number2
DOIs
Publication statusPublished - Feb 2021

Keywords

  • VACUUM INTERFACE PROBLEM
  • CURRENT-VORTEX SHEETS
  • EULER EQUATIONS
  • LOCAL EXISTENCE
  • MOTION
  • STABILITY
  • LIQUID

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