Energy equality for the isentropic compressible Navier-Stokes equations without upper bound of the density

Abstract: In this paper, we are concerned with the minimal regularity of both the density and the velocity for the weak solutions keeping energy equality in the isentropic compressible Navier-Stokes equations. The energy equality criteria without upper bound of the density are established. Almost all previous corresponding results requires $$\rho\in L<sup>{\infty}(0,T;L<sup>{\infty}(\mathbb{T}<sup>{d}))$$.