In this paper, we assume a density with integrability on the space L ∞(0, T; Lq0) 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.
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