scholarly journals Large-time behaviour of solutions to the outflow problem of full compressible Navier–Stokes equations

Nonlinearity ◽  
2011 ◽  
Vol 24 (5) ◽  
pp. 1369-1394 ◽  
Author(s):  
Xiaohong Qin
Keyword(s):  
Large Time ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Behaviour ◽  
Navier Stokes Equations ◽  
Large Time Behaviour

On the formation of weak plane shock waves by impulsive motion of a piston

1966 ◽  
Vol 25 (4) ◽  
pp. 705-718 ◽  
Author(s):  
John P. Moran ◽  
S. F. Shen
Keyword(s):  
Large Time ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Plane Shock ◽  
Heat Conducting ◽  
Piston Problem ◽  
Navier Stokes Equations ◽  
Viscous Heat ◽  
Equation Boundary ◽  
Weak Plane

The piston problem for a viscous heat-conducting gas is studied under the assumption that the piston Mach number ε is small. The linearized Navier–Stokes equations are found to be valid up to times of the order of ε−2mean free times after the piston is set in motion, while at large times the solution is governed by Burgers's equation. Boundary conditions for the large-time solution are supplied by the matching principle of the method of inner and outer expansions, which is also used to construct a composite solution valid both for small and for large times.

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