Preprint 1998-042

Large-time Behavior of Solutions to the Equations of a One-dimensional Viscous Polytropic Ideal Gas in Unbounded Domains

Song Jiang

Abstract: The large-time behavior of solutions to the initial and initial boundary value problems for a one-dimensional viscous polytropic ideal gas in unbounded domains is investigated. Using a special cut-off function to localize the problem, we derive a local representation for the specific volume. With the help of the local representation, and certain new estimates for the temperature and the stress, and the weighted energy estimates, we prove that in any bounded interval, the specific volume is pointwise bounded from below and above for all $t\geq 0$ and a generalized solution is convergent as time goes to infinity.

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Large-time behavior of solutions to the equations of a one-dimensional viscous polytropic ideal gas in unbounded domains
Song Jiang, <>, <>
Publishing information:
Accepted for publication in: Commun. Math. Phys.
Submitted by:
<> December 28 1998.

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