One-Dimensional Viscous and Heat-Conducting Ionized Gas with Density-dependent Viscosity

2021 ◽  
Vol 53 (5) ◽  
pp. 5580-5612
Author(s):  
Yongkai Liao ◽  
Huijiang Zhao ◽  
Jiawei Zhou
Keyword(s):  
Heat Conducting ◽  
Ionized Gas ◽  
One Dimensional ◽  
Density Dependent ◽  
Dependent Viscosity

scholarly journals One-dimensional compressible heat-conducting gas with temperature-dependent viscosity

2016 ◽  
Vol 26 (12) ◽  
pp. 2237-2275 ◽  
Author(s):  
Tao Wang ◽  
Huijiang Zhao
Keyword(s):  
Initial Data ◽  
Vacuum Solution ◽  
Viscosity Coefficient ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
One Dimensional ◽  
The One ◽  
Dependent Viscosity

We consider the one-dimensional compressible Navier–Stokes system for a viscous and heat-conducting ideal polytropic gas when the viscosity [Formula: see text] and the heat conductivity [Formula: see text] depend on the specific volume [Formula: see text] and the temperature [Formula: see text] and are both proportional to [Formula: see text] for certain non-degenerate smooth function [Formula: see text]. We prove the existence and uniqueness of a global-in-time non-vacuum solution to its Cauchy problem under certain assumptions on the parameter [Formula: see text] and initial data, which imply that the initial data can be large if [Formula: see text] is sufficiently small. Such a result appears to be the first global existence result for general adiabatic exponent and large initial data when the viscosity coefficient depends on both the density and the temperature.

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