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

Susan Friedlander, Vlad Vicol

Research output: Contribution to journalArticle

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

Fingerprint

Continuous Solution
Magnetohydrodynamics
regularity
Parabolic Equation
Weak Solution
Regularity
Nonlinear Parabolic Equations
Minimality
Energy Estimates
Besov Spaces
Classical Solution
magnetohydrodynamics
Space-time
Exponent
exponents
estimates
energy

Keywords

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

ASJC Scopus subject areas

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

Cite this

Higher regularity of hölder continuous solutions of parabolic equations with singular drift velocities. / Friedlander, Susan; Vicol, Vlad.

In: Journal of Mathematical Fluid Mechanics, Vol. 14, No. 2, 01.06.2012, p. 255-266.

Research output: Contribution to journalArticle

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