REGULARITY OF WEAK SOLUTIONS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

Title & Authors
REGULARITY OF WEAK SOLUTIONS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS
Choe, Hi-Jun; Jin, Bum-Ja;

Abstract
In this paper, we assume a density with integrability on the space $\small{L^{\infty}}$(0, T; $\small{L^{q_{0}}}$) for some $\small{q_{0}}$ 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 $\small{T^3}$ $\small{{\times}}$ (0, T). Moreover, Moser type iteration scheme is developed for $\small{L^{\infty}}$ norm estimate for the velocity.
Keywords
compressible;regularity;generalized solution;
Language
English
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