Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation

Luis Caffarelli; Alexis Vasseur

doi:http://doi.org/10.4007/annals.2010.171.1903

Abstract

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.

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Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation

Abstract

Authors