Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
Analysis of PDEs
2007-05-23 v1
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 (-\Delta)^{1/2}, are locally smooth for any space dimension.
Cite
@article{arxiv.math/0608447,
title = {Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation},
author = {L. Caffarelli and A. Vasseur},
journal= {arXiv preprint arXiv:math/0608447},
year = {2007}
}
Comments
25 pages