scholarly journals Global solvability of the initial-boundary value problem for Navier–Stokes–Fourier type equations describing flows of viscous compressible heat-conducting multifluids

2019 ◽  
Vol 1268 ◽  
pp. 012061
Author(s):  
Alexander Mamontov ◽  
Dmitry Prokudin
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Solvability ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Initial Boundary Value ◽  
Fourier Type

The initial–boundary-value problem for real viscous heat-conducting flow with shear viscosity

2003 ◽  
Vol 133 (4) ◽  
pp. 969-986 ◽  
Author(s):  
Dehua Wang
Keyword(s):  
Initial Data ◽  
Boundary Value Problem ◽  
Shear Viscosity ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Heat Conducting ◽  
Large Initial Data ◽  
Viscous Heat ◽  
Initial Boundary Value

An initial–boundary-value problem for the nonlinear equations of real compressible viscous heat-conducting flow with general large initial data is investigated. The main point is to study the real flow for which the pressure and internal energy have nonlinear dependence on temperature, unlike the linear dependence for ideal flow, and the viscosity coefficients and heat conductivity are also functions of density and/or temperature. The shear viscosity is also presented. The existence, uniqueness and regularity of global solutions are established with large initial data in H1. It is shown that there is no shock wave, vacuum, mass concentration, or heat concentration (hot spots) developed in a finite time, although the solutions have large oscillations.

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