A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators

Sylvia Serfaty, Juan Luis Vázquez

Research output: Contribution to journalArticle

Abstract

In the limit of a nonlinear diffusion model involving the fractional Laplacian we get a "mean field" equation arising in superconductivity and superfluidity. For this equation, we obtain uniqueness, universal bounds and regularity results. We also show that solutions with finite second moment and radial solutions admit an asymptotic large time limiting profile which is a special self-similar solution: the "elementary vortex patch".

Original languageEnglish (US)
Pages (from-to)1091-1120
Number of pages30
JournalCalculus of Variations and Partial Differential Equations
Volume49
Issue number3-4
DOIs
StatePublished - Mar 2014

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Universal Bounds
Superfluidity
Fractional Laplacian
Large Time Asymptotics
Mean Field Equation
Radial Solutions
Nonlinear Diffusion
Self-similar Solutions
Superconductivity
Diffusion Model
Patch
Nonlinear Model
Vortex
Uniqueness
Limiting
Regularity
Moment
Superfluid helium
Vortex flow
Profile

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators. / Serfaty, Sylvia; Vázquez, Juan Luis.

In: Calculus of Variations and Partial Differential Equations, Vol. 49, No. 3-4, 03.2014, p. 1091-1120.

Research output: Contribution to journalArticle

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