We study the two-dimensional beta-generalized supercritical quasi- geostrophic equation, and in particular show that to obtain global regularity results, one needs to bound only its partial derivative. Results may be gener- alized to similar active scalars, e.g. the porous media equation.
|Journal||Electronic Journal of Differential Equations|
|State||Published - Sep 30 2013|
- Porous media equation
- Quasi-geostrophic equation
- Regularity criteria