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

Susan Friedlander; Vlad Vicol

doi:10.1016/j.anihpc.2011.01.002

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

Susan Friedlander, Vlad Vicol

Mathematics

Research output: Contribution to journal › Article › peer-review

64 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 L_t ^∞BMO_x^-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 language	English (US)
Pages (from-to)	283-301
Number of pages	19
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	28
Issue number	2
DOIs	https://doi.org/10.1016/j.anihpc.2011.01.002
State	Published - 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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10.1016/j.anihpc.2011.01.002

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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.",

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pages = "283--301",

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AU - Friedlander, Susan

AU - Vicol, Vlad

PY - 2011

Y1 - 2011

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

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JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 2

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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