  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 $L^2(0,T;
B^{1/2}_{2,c(\mathbb N)})$ satisfies energy equality.
