For the stationary compressible viscous Navier-Stokes equations with no-slip condition on a convex polygon
type: Item
instance of: scholarly article
title: For the stationary compressible viscous Navier-Stokes equations with no-slip condition on a convex polygon
zbMATH Open document ID: 1216.35084
author: Hyung Jun Choi
author: Jae Ryong Kweon
published in: Journal of Differential Equations
publication date: 2011-03-17T00:00:00Z
review text: The compressible viscous Navier-Stokes equations are considered in a convex polygonal domain \(D\subset{\mathbb R}^2\) \[ -\mu\Delta v+\rho (v\cdot\nabla) v-(\mu+\nu)\nabla\operatorname{div}v+ \nabla p(\rho)= \rho f,\quad \operatorname{div}(\rho v)=g, \] \[ v=0,\quad \text{on }\partial D. \] Here \(v\) is the velocity field, \(\rho\) is the density and \(p=p\,(\rho)\) is the pressure, \(\mu\) and \(\nu\) are the viscous numbers with \(\mu>0\) and \(\mu+\nu>0\), \(f\) and \(g\) are given functions. In this paper \(p\,(\rho)=\rho\). It is shown that the solution to the problem exists in a small neighborhood of \((0,\tilde{\rho})\) for any convex polygon. The size of the neighborhood is determined by the data of the problem \((f,g)\). The singular behavior of the solution is described by the eigenvalue problem of the Stokes operator with zero Dirichlet condition, [see, \textit{V. A. Kozlov, V. G. Maz'ya} and \textit{J. Rossmann}, Spectral problems associated with corner singularities of solutions to elliptic equations. Providence, RI: American Mathematical Society (AMS) (2001; Zbl 0965.35003)].
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 5867207
zbMATH Keywords: compressible viscous flows
zbMATH Keywords: corner singularity
zbMATH Keywords: convex polygon
zbMATH Keywords: Navier-Stokes equations
reviewed by: Il'ya Sh. Mogilevskii
MaRDI profile type: Publication
full work available at URL: j.jde.2010.12.018
OpenAlex ID: W2094419662
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DOI: 10.1016/J.JDE.2010.12.018
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description: scientific article; zbMATH DE number 5867207