Asymptotic behavior of solutions of initial-boundary value problems for 1D viscous and heat-conducting ionized gas
type: Item
instance of: scholarly article
title: Asymptotic behavior of solutions of initial-boundary value problems for 1D viscous and heat-conducting ionized gas
zbMATH Open document ID: 1503.35170
author: Yongkai Liao
author: Huijiang Zhao
published in: Journal of Differential Equations
publication date: 2022-11-28T00:00:00Z
review text: This work deals with the compressible Navier-Stokes equations with specific internal energy (for ionized gases) in Lagrangian coordinates in one space dimension. For a ionized gas, pressure and internal energy depend on \(\alpha\), which represents the degree of ionization. The viscosity is assumed to depend on the specific volume \(v\), and the thermal conductivity \(\kappa=\kappa(\theta, v)\) is a function of temperature \(\theta\) and specific volume \(v\). The authors provide a precise description of the large time behavior of the global solutions to this system, whose existence is due to their previous paper with \textit{J. Zhou} [SIAM J. Math. Anal. 53, No. 5, 5580--5612 (2021; Zbl 1480.35330)]. One of the main difficulties of this problem is the loss of concavity of the physical entropy in some small bounded domain, which is connected to the dependence of the state of an ionized gas on the degree of ionization. To overcome such issue, the authors provide new a priori estimates for the temperature \(\theta\) and the specific volume \(v\) that are uniform in time.
reviewed by: Roberta Bianchini
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 76N15
zbMATH DE Number: 7623964
zbMATH Keywords: large time behavior of global solutions
zbMATH Keywords: one-dimensional viscous and heat-conducting ionized gas
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: density-dependent viscosity
zbMATH Keywords: global large solutions
MaRDI profile type: Publication
full work available at URL: j.jde.2022.10.019
OpenAlex ID: W4307815802
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DOI: 10.1016/J.JDE.2022.10.019
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description: scientific article; zbMATH DE number 7623964