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

Susan Friedlander, Vlad Vicol

Research output: Contribution to journalArticle

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

Fingerprint

Drift-diffusion Equations
Global Regularity
Advection-diffusion Equation
Divergence-free
Global Well-posedness
Advection
Weak Solution
Turbulence
Scalar
Fluid
Earth (planet)
Fluids
Class
Context
Family

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics

Cite this

Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics. / Friedlander, Susan; Vicol, Vlad.

In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 28, No. 2, 01.01.2011, p. 283-301.

Research output: Contribution to journalArticle

@article{5238bd7ddd6f4a3885dd996857ae41da,
title = "Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics",
abstract = "We use De Giorgi techniques to prove H{\"o}lder 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.",
keywords = "De Giorgi, Global regularity, Magneto-geostrophic equations, Parabolic equations, Weak solutions",
author = "Susan Friedlander and Vlad Vicol",
year = "2011",
month = "1",
day = "1",
doi = "10.1016/j.anihpc.2011.01.002",
language = "English (US)",
volume = "28",
pages = "283--301",
journal = "Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis",
issn = "0294-1449",
publisher = "Elsevier Masson SAS",
number = "2",

}

TY - JOUR

T1 - Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics

AU - Friedlander, Susan

AU - Vicol, Vlad

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

KW - De Giorgi

KW - Global regularity

KW - Magneto-geostrophic equations

KW - Parabolic equations

KW - Weak solutions

UR - http://www.scopus.com/inward/record.url?scp=79953029001&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953029001&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2011.01.002

DO - 10.1016/j.anihpc.2011.01.002

M3 - Article

VL - 28

SP - 283

EP - 301

JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

SN - 0294-1449

IS - 2

ER -