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

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

2006-08-17

arxiv.org/abs/math/0608447v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

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.

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