Higher order commutator estimates and local existence for the non-resistive MHD equations and related models

Charles L. Fefferman, David S. McCormick, James C. Robinson, Jose L. Rodrigo

Research output: Contribution to journalArticle

72 Scopus citations

Abstract

This paper establishes the local-in-time existence and uniqueness of strong solutions in Hs for s>n/2 to the viscous, non-resistive magnetohydrodynamics (MHD) equations in Rn, n=2, 3, as well as for a related model where the advection terms are removed from the velocity equation. The uniform bounds required for proving existence are established by means of a new estimate, which is a partial generalisation of the commutator estimate of Kato and Ponce (1988) [13].

Original languageEnglish (US)
Pages (from-to)1035-1056
Number of pages22
JournalJournal of Functional Analysis
Volume267
Issue number4
DOIs
StatePublished - Aug 15 2014

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Commutator estimates
  • MHD
  • Magnetohydrodynamics

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