Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics

Susan Friedlander, Vlad Vicol

Research output: Contribution to journalArticle

44 Scopus citations

Abstract

We use De Giorgi techniques to prove Hölder continuity of weak solutions to a class of drift-diffusion equations, with L2 initial data and divergence free drift velocity that lies in Lt BMOx-1. We apply this result to prove global regularity for a family of active scalar equations which includes the advection-diffusion equation that has been proposed by Moffatt in the context of magnetostrophic turbulence in the Earths fluid core.

Original languageEnglish (US)
Pages (from-to)283-301
Number of pages19
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume28
Issue number2
DOIs
StatePublished - Jan 1 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

Keywords

  • De Giorgi
  • Global regularity
  • Magneto-geostrophic equations
  • Parabolic equations
  • Weak solutions

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