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

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 ra...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 49; no. 3-4; pp. 1091 - 1120
Main Authors Serfaty, Sylvia, Vázquez, Juan Luis
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2014
Springer Nature B.V
Subjects
Analysis
Asymptotic properties
Calculus of variations
Calculus of Variations and Optimal Control; Optimization
Constraining
Control
Diffusion
Fractions
Laplace transforms
Mathematical analysis
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinear equations
Nonlinearity
Partial differential equations
Self-similarity
Superconductivity
Systems Theory
Theoretical
76S05
35K55
35K65
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Summary: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”.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-013-0613-9