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

Published online by Cambridge University Press:  12 July 2007

Song Jiang
Song Jiang
Affiliation:
LCP, Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, People's Republic of China (jiang@mail.iapcm.ac.cn)
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Abstract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 3 , June 2002 , pp. 627 - 638
Copyright
Copyright © Royal Society of Edinburgh 2002

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