The super-critical dissipative quasi-geostrophic equations with dispersive forcing

Abstract

This paper derive regularity criteria for the super-critical dissipative quasi-geostrophic equations with dispersive forcing. These criteria generalized the corresponding regularity conditions of critical dissipative quasi-geostrophic equations to the super-critical case with dispersive term. It is showed here that the super-critical dissipative quasi-geostrophic equations admit a unique global smooth solution when the prescribed initial data satisfies equation for sufficient small number C ∝ > 0.