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

Access to Document

10.1016/j.anihpc.2011.01.002

Cite this

@article{f7fcb27b51aa49f098be7dc2bef9308f,

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",

doi = "10.1016/j.anihpc.2011.01.002",

language = "English (US)",

volume = "28",

pages = "283--301",

journal = "Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire",

issn = "0294-1449",

publisher = "European Mathematical Society Publishing House",

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

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

UR - https://www.scopus.com/pages/publications/79953029001

UR - https://www.scopus.com/pages/publications/79953029001#tab=citedBy

U2 - 10.1016/j.anihpc.2011.01.002

DO - 10.1016/j.anihpc.2011.01.002

M3 - Article

AN - SCOPUS:79953029001

SN - 0294-1449

VL - 28

SP - 283

EP - 301

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

Access to Document

Other files and links

Fingerprint

Cite this