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

• 成果类型: Article
• 署名作者: Caffarelli, Luis A.; Vasseur, Alexis
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 1903-1930
• 关键词: global well-posedness; REGULARITY; BEHAVIOR

摘要

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.