Asymptotic behavior of solutions of initial-boundary value problems for 1D viscous and heat-conducting ionized gas
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.
one-dimensional viscous and heat-conducting ionized gas
scientific article; zbMATH DE number 7623964
scientific article