REGULARITY OF WEAK SOLUTIONS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS Choe, Hi-Jun; Jin, Bum-Ja;
In this paper, we assume a density with integrability on the space (0, T; ) for some 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 (0, T). Moreover, Moser type iteration scheme is developed for norm estimate for the velocity.