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

作者：Caffarelli Luis A^*; Vasseur Alexis

来源：Annals of Mathematics, 2010, 171(3): 1903-1930.

DOI：10.4007/annals.2010.171.1903

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. (-Delta)(1/2) are locally smooth for any space dimension.

• 出版日期2010-5