Existence, uniqueness, and computation of solutions for mixed problems in compressible fluid flow
type: Item
instance of: scholarly article
title: Existence, uniqueness, and computation of solutions for mixed problems in compressible fluid flow
zbMATH Open document ID: 0777.35063
DOI: 10.1016/0022-247X(92)90094-T
author: Roger E. Zarnowski
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-05-16T00:00:00Z
review text: Initial-boundary value problems are considered for the one-dimensional Navier-Stokes equations for compressible flow on a finite interval. Convergence of finite difference schemes are proved for each of three different cases of initial and boundary data. For BV discontinuous initial data that is piecewise smooth the density is shown to remain discontinuous and a bound is given for the error of an approximate solution in a norm that dominates the sup-norm of the density. For \(H^ 1\) initial data a different error bound is given in the same norm.
reviewed by: Alan Jeffrey
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 168003
zbMATH Keywords: initial-boundary value problems
zbMATH Keywords: \(H^ 1\) initial data
zbMATH Keywords: convergence of finite difference schemes
zbMATH Keywords: one-dimensional Navier-Stokes equations
zbMATH Keywords: compressible flow
zbMATH Keywords: discontinuous initial data
MaRDI profile type: Publication
cites work: Q3786181
cites work: Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data
cites work: Global Existence for 1D, Compressible, Isentropic Navier-Stokes Equations with Large Initial Data
cites work: Mixed problems for nonlinear conservation laws
cites work: Q4746129
cites work: A Finite-Difference Scheme for the Navier–Stokes Equations of One-Dimensional, Isentropic, Compressible Flow
description: scientific article; zbMATH DE number 168003