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

L. Caffarelli; A. Vasseur

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

L. Caffarelli·A. Vasseur

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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 Holder continuous. As an application we show that solutions of the quasi-geostrophic equation with initial L^2 data and critical diffusion (-Δ)^{1/2}, are locally smooth for any space dimension.

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L. Caffarelli, A. Vasseur. 2006-08-17. Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. https://arxiv.org/abs/math/0608447

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