Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 217, pp. 1-12.

Title: Regularity criteria of supercritical beta-generalized quasi-geostrophic
        equations in terms of partial derivatives

Author: Kazuo Yamazaki (Oklahoma State Univ., Stillwater, OK, USA)

Abstract:
 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 generalized to similar active scalars, e.g. the porous media
 equation.

Submitted June 25, 2013. Published September 30, 2013.
Math Subject Classifications: 35B65, 35Q35, 35Q86.
Key Words: Quasi-geostrophic equation; porous media equation; regularity criteria.