Analysis of semidiscretization of the compressible Navier-Stokes equations

Abstract

The objective of this work is to present the existence result for the evolu- tionary compressible Navier-Stokes equations via time discretization. We consider the two-dimensional case with slip boundary conditions. First, the existence of weak solution for a fixed time step Δt > 0 is presented and then the limit passage as Δt \to 0+ is carried out. The proof is based on a new technique established for the stedy Navier-Stokes equations by Mucha P. and Pokorný M. 2006 Nonlinearity 19 1747-1768.

arXiv comment31 pages