Local Existence for the Non-Resistive MHD Equations in Nearly Optimal Sobolev Spaces

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

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in Rd, where d = 2, 3, with initial data B0∈ Hs(Rd) and u0∈ Hs - 1 + ϵ(Rd) for s> d/ 2 and any 0 < ϵ< 1. The proof relies on maximal regularity estimates for the Stokes equation. The obstruction to taking ϵ= 0 is explained by the failure of solutions of the heat equation with initial data u0∈ Hs - 1 to satisfy u∈ L1(0 , T; Hs + 1) ; we provide an explicit example of this phenomenon.

Original languageEnglish (US)
Pages (from-to)677-691
Number of pages15
JournalArchive for Rational Mechanics and Analysis
Volume223
Issue number2
DOIs
StatePublished - Feb 1 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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