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

This paper derive regularity criteria for the supercritical 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 ||∇θ₀||_L∞^1-2α ||θ₀||_L∞^2α <; C_α for sufficient small number C_α > 0.