English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we investigate the issue of the inviscid limit for thecompressible Navier-Stokes system in an impermeable fixed bounded domain. Weconsider two kinds of boundary conditions. The first one is the no-slipcondition. In this case we extend the famous conditional result obtained byKato in the homogeneous incompressible case. Kato proved that if the energydissipation rate of the viscous flow in a boundary layer of width proportionalto the viscosity vanishes then the solutions of the incompressibleNavier-Stokes equations converge to some solutions of the incompressible Eulerequations in the energy space. We provide here a natural extension of thisresult to the compressible case. The other case is the Navier condition whichencodes that the fluid slips with some friction on the boundary. In this casewe show that the convergence to the Euler equations holds true in the energyspace, as least when the friction is not too large. In both cases we use in acrucial way some relative energy estimates proved recently by Feireisl, Ja Jinand Novotn{\'y}.

On the inviscid limit for the compressible Navier-Stokes system in an impermeable bounded domain