Electron. J. Diff. Equ., Vol. 2013 (2013), No. 217, pp. 1-12.

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

Kazuo Yamazaki

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.

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Kazuo Yamazaki
Department of Mathematics, Oklahoma State University
401 Mathematical Sciences, Stillwater, OK 74078, USA
email: kyamazaki@math.okstate.edu

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