scholarly journals Viscous Limits to Piecewise Smooth Solutions for the Navier-Stokes Equations of One-dimensional Compressible Viscous Heat-conducting Fluids

2009 ◽  
Vol 16 (1) ◽  
pp. 1-32
Author(s):  
Shixiang Ma
Keyword(s):  
Stokes Equations ◽  
Piecewise Smooth ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Smooth Solutions ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Viscous Heat ◽  
Heat Conducting Fluids ◽  
Conducting Fluids

BLOW-UP OF SMOOTH SOLUTIONS TO THE NAVIER–STOKES EQUATIONS OF COMPRESSIBLE VISCOUS HEAT-CONDUCTING FLUIDS

2010 ◽  
Vol 88 (2) ◽  
pp. 239-246 ◽  
Author(s):  
ZHONG TAN ◽  
YANJIN WANG
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Initial Density ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Smooth Solutions ◽  
Navier Stokes Equations ◽  
The Cauchy Problem ◽  
Heat Conducting Fluids ◽  
Conducting Fluids

AbstractWe give a simpler and refined proof of some blow-up results of smooth solutions to the Cauchy problem for the Navier–Stokes equations of compressible, viscous and heat-conducting fluids in arbitrary space dimensions. Our main results reveal that smooth solutions with compactly supported initial density will blow up in finite time, and that if the initial density decays at infinity in space, then there is no global solution for which the velocity decays as the reciprocal of the elapsed time.

scholarly journals NUMERICAL CALCULATION OF CONVECTIVE FLOW OF GAS AT CIRCULAR-TYPE SCHEME OF HEATING

2015 ◽  
pp. 87-93
Author(s):  
E. M. Sorokina ◽  
A. G. Obukhov
Keyword(s):  
Convective Flow ◽  
Stokes Equations ◽  
Complete System ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Boundary Condi Tions ◽  
Navier Stokes Equations ◽  
Viscous Heat ◽  
Condi Tions

To investigate the convective flows of polytropic gas a complete system of Navier - Stokes equations is consid-ered. As the initial and boundary conditions the specific ratios are offered. The proposed initial and boundary condi-tions realization is carried out at construction of the numerical solution of the complete system of Navier - Stokes equations for modeling the unsteady state three-dimensional convection flows of the compressible viscous heat-conducting gas in the isolated cubic area. Three components of the velocity vector are calculated for the initial stage of the convective flow. It is shown that the velocity components are complex and depend essentially on the heating shape, height and time.

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