Asymptotic behaviour of the density for one-dimensional Navier-Stokes equations
type: Item
instance of: scholarly article
title: Asymptotic behaviour of the density for one-dimensional Navier-Stokes equations
zbMATH Open document ID: 0687.35074
DOI: 10.1007/BF01357718
author: I. Straškraba
author: Alberto Valli
published in: Manuscripta Mathematica
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155356
review text: The paper addresses the question of global (in time) existence of a solution to the Navier-Stokes equation, for a barotropic (compressible) fluid, on a one-dimensional bounded domain. The authors show that this problem has a global solution if the external force is time independent, moreover they show that the density is bounded away from zero below and bounded above provided that the external force and pressure satisfy a certain compatibility condition. This compatibility condition holds if the external force is sufficiently small. If this compatibility condition does not hold the density becomes zero or infinite asymptotically.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 4125948
zbMATH Keywords: global solution
zbMATH Keywords: barotropic compressible fluid
reviewed by: A. J. Meir
MaRDI profile type: Publication
cites work: Q3685389
cites work: An \(L^ p\)-theory for the \(n\)-dimensional, stationary, compressible Navier-Stokes equations, and the incompressible limit for compressible fluids. The equilibrium solutions
cites work: On the temporally global problem of the generalized Burgers' equation
cites work: Q3657645
cites work: Q3955052
cites work: Q3329854
OpenAlex ID: W2053060161
description: scientific article; zbMATH DE number 4125948