Global symmetric classical solutions for radiative compressible Navier‐Stokes equations with temperature‐dependent viscosity coefficients

2020 ◽  
Author(s):  
Boran Zhu
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Navier Stokes Equations ◽  
Viscosity Coefficients ◽  
Dependent Viscosity

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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