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

  • Date: 12/12/2006

Alexis Vasseur (University of Texas )


University of British Columbia


The critical dissipative quasi-geostrophic equation was proposed by
several authors as a toy model to study the regularity of solutions to
3D Navier-Stokes equations. In this work, in collaboration with L.
Caffarelli, we prove that drift-diffusion equatons with L2 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 L2 data and critical diffusion (-Delta)^{1/2}, are locally
smooth for any space dimension.

Other Information: 

DG-MP-PDE Seminar 2006