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

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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 gener- alized to similar active scalars, e.g. the porous media equation.

Original languageEnglish
JournalElectronic Journal of Differential Equations
Volume2013
StatePublished - Sep 30 2013

Keywords

  • Porous media equation
  • Quasi-geostrophic equation
  • Regularity criteria

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