Remarks on the asymptotic behaviour of solutions to the compressible Navier–Stokes equations in the half-line

2002 ◽  
Vol 132 (03) ◽  
pp. 627
Keyword(s):  
Asymptotic Behaviour ◽  
Stokes Equations ◽  
Half Line ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Asymptotic Behaviour Of Solutions

Remarks on the asymptotic behaviour of solutions to the compressible Navier–Stokes equations in the half-line

2002 ◽  
Vol 132 (3) ◽  
pp. 627-638 ◽  
Author(s):  
Song Jiang
Keyword(s):  
Asymptotic Behaviour ◽  
Specific Volume ◽  
Stokes Equations ◽  
Global Solutions ◽  
Ideal Gas ◽  
Half Line ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Asymptotic Behaviour Of Solutions

We study the time-asymptotic behaviour of solutions to the Navier-Stokes equations for a one-dimensional viscous polytropic ideal gas in the half-line. Using a local representation for the specific volume, which is obtained by using a special cut-off function to localize the problem, and the weighted energy estimates, we prove that the specific volume is pointwise bounded from below and above for all x, t and that for all t the temperature is bounded from below and above locally in x. Moreover, global solutions are convergent as time goes to infinity. The large-time behaviour of solutions to the Cauchy problem is also examined.

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