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 language||English (US)|
|Number of pages||30|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Mar 2014|
ASJC Scopus subject areas
- Applied Mathematics