Regularity criterion and energy conservation for the supercritical Quasi-Geostrophic equation

Abstract

This paper studies the regularity and energy conservation problems for the 2D supercritical quasi-geostrophic (SQG) equation. We apply an approach of splitting the dissipation wavenumber to obtain a new regularity condition which is weaker than all the Prodi-Serrin type regularity conditions. Moreover, we prove that any weak solution of the supercritical SQG in $L^2(0,T;B_{2,c(\mathbb{N})}^{1/2})$ satisfies energy equality.

Typo fixed. Accepted to the Journal of Mathematical Fluid Mechanics

References in corpus (2)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Eventual Regularity of the Solutions to the Supercritical Dissipative Quasi-Geostrophic Equation

Cited by in corpus (3)

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• Regularity criterion for the 3D Hall-magneto-hydrodynamics