Analysis of semidiscretization of the compressible Navier-Stokes equations

Details Analysis of semidiscretization of the compressible Navier-Stokes equations Analysis of semidiscretization of the compressible Navier-Stokes equations

2010-09-16

arxiv.org/abs/1009.3141v1

Mathematics

Classical Analysis and ODEs

31 pages

Scientific paper

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 \Delta t > 0 is presented and then the limit passage as \Delta t \to 0+ is carried out. The proof is based on a new technique established for the stedy Navier-Stokes equations by Mucha P. and Pokorn\'y M. 2006 Nonlinearity 19 1747-1768.

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