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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)})) satisfies energy equality.

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