Drift diffusion equations with fractional diffusion and the quasigeostrophic equation
Abstract
Motivated by the critical dissipative quasigeostrophic equation, we prove that driftdiffusion 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 quasigeostrophic equation with initial L^2 data and critical diffusion (\Delta)^{1/2}, are locally smooth for any space dimension.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2006
 DOI:
 10.48550/arXiv.math/0608447
 arXiv:
 arXiv:math/0608447
 Bibcode:
 2006math......8447C
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 25 pages