Nonlinear stability of viscous shock profiles for compressible Navier–Stokes equations with temperature-dependent transport coefficients and large initial perturbation

2018 ◽  
Vol 69 (6) ◽  
Author(s):  
Bingkang Huang ◽  
Shaojun Tang ◽  
Lan Zhang
Keyword(s):  
Nonlinear Stability ◽  
Stokes Equations ◽  
Transport Coefficients ◽  
Initial Perturbation ◽  
Navier Stokes ◽  
Temperature Dependent ◽  
Navier Stokes Equations ◽  
Shock Profiles ◽  
Dependent Transport ◽  
Large Initial Perturbation

scholarly journals On the Navier-Stokes equations with temperature-dependent transport coefficients

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Eduard Feireisl ◽  
Josef Málek
Keyword(s):  
Stokes Equations ◽  
Transport Coefficients ◽  
Three Dimensional ◽  
Periodic Problem ◽  
Large Data ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Long Time ◽  
Spatially Periodic ◽  
Dependent Transport

We establish long-time and large-data existence of a weak solution to the problem describing three-dimensional unsteady flows of an incompressible fluid, where the viscosity and heat-conductivity coefficients vary with the temperature. The approach reposes on considering the equation for the total energy rather than the equation for the temperature. We consider the spatially periodic problem.

The limit to rarefaction wave with vacuum for 1D compressible fluids with temperature-dependent transport coefficients

2015 ◽  
Vol 13 (05) ◽  
pp. 555-589 ◽  
Author(s):  
Mingjie Li ◽  
Teng Wang ◽  
Yi Wang
Keyword(s):  
Heat Conduction ◽  
Rarefaction Wave ◽  
Stokes Equations ◽  
Transport Coefficients ◽  
Vacuum State ◽  
Navier Stokes ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Navier Stokes Equations ◽  
Heat Conduction Coefficient

In this paper, we study the zero dissipation limit of the one-dimensional full compressible Navier–Stokes equations with temperature-dependent viscosity and heat-conduction coefficient. It is proved that given a rarefaction wave with one-side vacuum state to the full compressible Euler equations, we can construct a sequence of solutions to the full compressible Navier–Stokes equations which converge to the above rarefaction wave with vacuum as the viscosity and the heat-conduction coefficient tend to zero. Moreover, the uniform convergence rate is obtained. The main difficulty in our proof lies in the degeneracies of the density, the temperature and the temperature-dependent viscosities at the vacuum region in the zero dissipation limit.

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