  We study the energy balance for weak solutions of the three-dimensional
compressible Navier--Stokes equations in a bounded domain. We establish an
$L^p$-$L^q$ regularity conditions on the velocity field for the energy equality
to hold, provided that the density is bounded and satisfies $\sqrt{\rho} \in
L^\infty_t H^1_x$. The main idea is to construct a global mollification
combined with an independent boundary cut-off, and then take a double limit to
prove the convergence of the resolved energy.
