Navier's slip and incompressible limits in domains with variable bottoms
type: Item
instance of: scholarly article
title: Navier's slip and incompressible limits in domains with variable bottoms
zbMATH Open document ID: 1159.35054
author: Eduard Feireisl
author: Josef Málek
author: Antonín Novotný
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2008-10-30T00:00:00Z
review text: The authors consider heat conducting compressible viscous Stokesian fluids in a domain with a flat top and a variable bottom. The actual rough boundary is approximated by a smooth one by imposing a slip boundary condition on the tangential component of the velocity vector whose normal component vanishes on the smooth boundary. The field equations and boundary conditions involve a small parameter related to the Mach number. Heat conduction is governed by Fourier's law. Shear and bulk viscosity and heat conduction coefficients are assumed to be Lipschitz function of the temperature. It is further supposed that viscous dissipation gives rise to a heat flux at the boundary. The governing differential equations are transformed into integral forms that allow the introduction of weak solutions. By employing various properties of certain Lebesgue and Sobolev spaces, it has been shown that the weak solution of the system in question converges asymptotically to the weak solution corresponding to an incompressible fluid flow with no-slip boundary condition for vanishingly small Mach numbers. Acoustical approximation is also dealt with details.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 76N17
Mathematics Subject Classification ID: 76E20
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 5359512
zbMATH Keywords: compressible thermoviscous flow
zbMATH Keywords: Oberbeck-Boussinesq approximation
zbMATH Keywords: slip boundary conditions
zbMATH Keywords: low Mach number limit
zbMATH Keywords: weak solutions
reviewed by: Erdoğan S. Şuhubi
MaRDI profile type: Publication
Wikidata QID: Q59316610
full work available at URL: dcdss.2008.1.427
OpenAlex ID: W2320389765
DOI: 10.3934/DCDSS.2008.1.427
description: scientific article; zbMATH DE number 5359512