Regularity of weak solutions of the compressible Navier-Stokes equations

In this paper, we assume a density with integrability on the space L ^∞(0, T; L^q0) for some q₀ and T > 0. Under the assumption on the density, we obtain a regularity result for the weak solutions to the compressible Navier-Stokes equations. That is, the supremum of the density is finite and the infimum of the density is positive in the domain T³ × X (0, T). Moreover, Moser type iteration scheme is developed for L^∞ norm estimate for the velocity.