# Regularity Criterion and Energy Conservation for the Supercritical Quasi-geostrophic Equation

@article{Dai2015RegularityCA, title={Regularity Criterion and Energy Conservation for the Supercritical Quasi-geostrophic Equation}, author={Mimi Dai}, journal={Journal of Mathematical Fluid Mechanics}, year={2015}, volume={19}, pages={191-202} }

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 viscosity solution of the supercritical SQG in $$L^2(0,T; B^{1/2}_{2,c(\mathbb N)})$$L2(0,T;B2,c(N)1/2) satisfies energy equality.

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