scholarly journals Global Classical Large Solutions to Navier--Stokes Equations for Viscous Compressible and Heat-Conducting Fluids with Vacuum

2013 ◽  
Vol 45 (2) ◽  
pp. 431-468 ◽  
Author(s):  
Huanyao Wen ◽  
Changjiang Zhu
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Large Solutions ◽  
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 PARALLEL COMPUTATIONS IN STUDIES OF DEPENDENCE OF GAS DYNAMIC PARAMETERS OF UPWARD SWIRLING FLOW OF GAS ON BLOWING VELOCITY

2016 ◽  
pp. 92-97
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Stokes Equations ◽  
Swirling Flow ◽  
Initial Conditions ◽  
Exact Analytical Solution ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Computational Domain ◽  
Navier Stokes Equations ◽  
Gas Dynamic

The rectangular parallelepiped explicit difference schemes for the numerical solution of the complete built system of Navier-Stokes equations. These solutions describe the three-dimensional flow of a compressible viscous heat-conducting gas in a rising swirling flows, provided the forces of gravity and Coriolis. This assumes constancy of the coefficient of viscosity and thermal conductivity. The initial conditions are the features that are the exact analytical solution of the complete Navier-Stokes equations. Propose specific boundary conditions under which the upward flow of gas is modeled by blowing through the square hole in the upper surface of the computational domain. A variant of parallelization algorithm for calculating gas dynamic and energy characteristics. The results of calculations of gasdynamic parameters dependency on the speed of the vertical blowing by the time the flow of a steady state flow.

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