Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
复制标题
DOI：
10.4007/annals.2010.171.1903
复制
发表时间：
2006-08
影响因子：
4.9
通讯作者：
L. Caffarelli;A. Vasseur
中科院分区：
文献类型：
--
作者：
L. Caffarelli;A. Vasseur
在临界耗散准地转方程的激励下，证明了具有L 2初值和漂移极小假设的漂移扩散方程是局部Holder连续的。作为应用，我们证明了具有L 2初值和临界扩散(-Δ)1/2的拟地转方程解在任意空间维都是局部光滑的。
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.