Existence of solutions of stationary compressible Navier-Stokes equations with large force
type: Item
instance of: scholarly article
title: Existence of solutions of stationary compressible Navier-Stokes equations with large force
zbMATH Open document ID: 0970.35094
author: Hi Jun Choe
author: Bum Ja Jin
published in: Journal of Functional Analysis
publication date: 2001-10-10T00:00:00Z
review text: The authors show an existence result for the stationary Navier-Stokes equations for isoentropic compressible flows in a bounded domain, with no-slip boundary conditions. The body force is arbitrary: it is not a potential force and there is no smallness assumption on it. But there is a smallness assumption on the Mach number. The pressure is given by \[ p=C\rho^\gamma,\qquad \gamma\geq 1. \] First the authors obtain a dimensionless form of the equations. They split the density into a constant average term \(\overline\rho\) and a fluctuation \(\varepsilon^2\rho\), where \(\varepsilon\) is the Mach number. By means of this splitting, they also split the system in two new ones. The first one are the incompressible Navier-Stokes equations forced by \(\overline\rho f\), so that it contains most of the external force. The second one are the compressible Navier-Stokes equations, forced by \(\varepsilon^2F\), where \(F\) is a body force which depends on \(f\) and on the solution of the incompressible equations. At the end the Leray-Schauder fixed point theorem is applied, under the smallness assumption of the Mach number. Finally the authors show that the found solutions converge, up to a subsequence, to the solution of the incompressible equations, as the Mach number goes to zero.
reviewed by: Marco Romito
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 1542414
zbMATH Keywords: compressible Navier-Stokes equations
zbMATH Keywords: existence with arbitrary force
zbMATH Keywords: incompressible limit
MaRDI profile type: Publication
full work available at URL: jfan.2000.3639
OpenAlex ID: W2052728445
cites work: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
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: Stationary Solutions of Compressible Navier–Stokes Equations with Slip Boundary Conditions
cites work: Symmetric positive linear differential equations
cites work: Q4292463
cites work: On the Cauchy problem for the system of fundamental equations describing the movement of compressible viscous fluid
cites work: On the temporally global problem of the generalized Burgers' equation
cites work: Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas
cites work: On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid
cites work: Q4389323
cites work: The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids
cites work: Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids
cites work: Existence and uniqueness for viscous steady compressible motions
cites work: On the first initial-boundary value problem of compressible viscous fluid motion
cites work: Q3329854
cites work: On the existence of stationary solutions to compressible Navier-Stokes equations
DOI: 10.1006/JFAN.2000.3639
Recommended article: Existence of strong solutions to the stationary compressible Navier-Stokes-Korteweg equations with large external force
Recommended article: On the existence of stationary solutions to compressible Navier-Stokes equations
Recommended article: Existence of solutions for the compressible Navier-Stokes equations
Recommended article: Existence and stability of stationary solutions to the compressible Navier-Stokes-Poisson equations
Recommended article: Q3824019
Recommended article: Stationary solutions to the compressible Navier-Stokes system with general boundary conditions
Recommended article: Existence of strong solutions to the steady Navier-Stokes equations for a compressible heat-conductive fluid with large forces
Recommended article: Existence of radially symmetric stationary solutions for the compressible Navier-Stokes equation
Recommended article: Large time behavior of solutions to the compressible Navier-Stokes equations with potential force
Recommended article: Compressible Navier-Stokes system: large solutions and incompressible limit
description: scientific article; zbMATH DE number 1542414