Asymptotic stability of viscous shock wave for a one-dimensional isentropic model of viscous gas with density dependent viscosity
type: Item
instance of: scholarly article
title: Asymptotic stability of viscous shock wave for a one-dimensional isentropic model of viscous gas with density dependent viscosity
zbMATH Open document ID: 1242.76059
author: Akitaka Matsumura
author: Yang Wang
published in: Methods and Applications of Analysis
publication date: 2011-07-22T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.maa/1306182407
review text: The authors investigate the asymptotic stability of viscous shock waves for a one-dimensional isentropic model of a viscous gas with density dependent viscosity by a weighted energy method developed in the papers of \textit{A. Matsumura} and \textit{M. Mei} [Osaka J. Math. 34, No. 3, 589--603 (1997; Zbl 0945.74539)] and \textit{I. Hashimoto} and \textit{A. Matsumura} [Methods Appl. Anal. 14, No. 1, 45--59 (2007; Zbl 1149.35057)]. Under the condition that the viscosity coefficient is given as a function of the absolute temperature which is determined by the Chapman-Enskog expansion theory in rarefied gas dynamics, any viscous shock wave is shown to be asymptotically stable for small initial perturbations with integral zero. This generalizes the previous result of \textit{A. Matsumura} and \textit{K. Nishihara} [Japan J. Appl. Math. 2, 17--25 (1985; Zbl 0602.76080)] where the viscosity coefficient was given by a constant, and a restriction on strength of viscous shock wave was assumed. This also analytically assures the spectral stability in Zumbrun's theory for any viscous shock wave in the present specific case.
reviewed by: Titus Petrila
Mathematics Subject Classification ID: 76E17
Mathematics Subject Classification ID: 76L05
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 5930179
zbMATH Keywords: weighted energy method
zbMATH Keywords: Chapman-Enskog expansion theory
zbMATH Keywords: Zumbrun's theory
MaRDI profile type: Publication
DOI: 10.4310/MAA.2010.V17.N3.A3
description: scientific article; zbMATH DE number 5930179