Global regularity for the 3D compressible magnetohydrodynamics with general pressure

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Abstract

We address the compressible magnetohydrodynamics (MHD) equations in R3 and establish a blow-up criterion for the local-in-time smooth solutions in terms of the density only. Namely, if the density is away from vacuum (ρ = 0) and the concentration of mass (ρ = ∞), then a local-in-time smooth solution can be continued globally in time. The results generalise and strengthen the previous ones in the sense that there is no magnetic field present in the criterion and the assumption on the pressure is significantly relaxed. The proof is based on some new a priori estimates for three-dimensional compressible MHD equations. Copyright © 2022 American Institute of Mathematical Sciences. All rights reserved.

Original languageEnglish
Pages (from-to)2927-2943
JournalDiscrete and Continuous Dynamical Systems
Volume42
Issue number6
DOIs
Publication statusPublished - Jun 2022

Citation

Suen, A. (2022). Global regularity for the 3D compressible magnetohydrodynamics with general pressure. Discrete and Continuous Dynamical Systems, 42(6), 2927-2943. doi: 10.3934/dcds.2022004

Keywords

  • Regularity
  • Blow-up criteria
  • Compressible magnetohydrodynamics

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