On weak solutions and a covergent numerical scheme for the compressible Navier-Strokes Equations

Abstract

In this paper, the three-dimensional compressible Navier-Stokes equations are considered on a periodic domain. We propose a semi-discrete numerical scheme and derive a priori bounds that ensures that the resulting system of ordinary di erential equations is solvable for any h > 0. An a posteriori examination that density remain uniformly bounded away from 0 will establish that a subsequence of the numerical solutions converges to a weak solution of the compressible Navier-Stokes equations.