Higher regularity of hölder continuous solutions of parabolic equations with singular drift velocities

Susan Friedlander, Vlad Vicol

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Motivated by an equation arising in magnetohydrodynamics, we prove that Hölder continuous weak solutions of a nonlinear parabolic equation with singular drift velocity are classical solutions. The result is proved using the space-time Besov spaces introduced by Chemin and Lerner (J Differ Equ 121(2):314-328, 1995), combined with energy estimates, without any minimality assumption on the Hölder exponent of the weak solutions.

Original languageEnglish (US)
Pages (from-to)255-266
Number of pages12
JournalJournal of Mathematical Fluid Mechanics
Volume14
Issue number2
DOIs
StatePublished - Jun 1 2012

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Higher regularity
  • Magneto-geostrophic model
  • Space-time Besov spaces
  • Weak solutions

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