Geodesic
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
Luis Caffarelli1 ; Alexis Vasseur1
1 University of Texas at Austin<br/>Department of Mathematics<br/>1 University Station C1200<br/>Austin TX 78712-0257<br/>United States
Annals of mathematics, Tome 171 (2010) no. 3, pp. 1903-1930.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Motivated by the critical dissipative quasi-geostrophic equation, we prove that drift-diffusion equations with $L^2$ initial data and minimal assumptions on the drift are locally Hölder continuous. As an application we show that solutions of the quasi-geostrophic equation with initial $L^2$ data and critical diffusion $(-\Delta)^{1/2}$ are locally smooth for any space dimension.
DOI : 10.4007/annals.2010.171.1903

Luis Caffarelli 1 ; Alexis Vasseur 1

1 University of Texas at Austin<br/>Department of Mathematics<br/>1 University Station C1200<br/>Austin TX 78712-0257<br/>United States 
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Luis Caffarelli; Alexis Vasseur. Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Annals of mathematics, Tome 171 (2010) no. 3, pp. 1903-1930. doi : 10.4007/annals.2010.171.1903. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.1903/

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