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
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