Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
Abstract
Motivated by the critical dissipative quasi-geostrophic equation, we prove that drift-diffusion equations with L2 initial data and minimal assumptions on the drift are locally Holder continuous. As an application we show that solutions of the quasi-geostrophic equation with initial L2 data and critical diffusion (-)1/2, are locally smooth for any space dimension.
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