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Large-time behavior of solutions to the equations of a viscous polytropic ideal gas. (English) Zbl 0953.35119
Summary: First we prove for the equations of a viscous polytropic ideal gas in bounded annular domains in $$\mathbb{R}^n$$ $$(n=2,3)$$ that (generalized) spherically symmetric solutions decay to a constant state exponentially as time goes to infinity. Then we show that solutions of the Cauchy problem in $$\mathbb{R}$$ are asymptotically stable if the initial specific volume is close to a constant in $$L^\infty$$ and weighted $$L^2$$, the initial velocity is small in weighted $$L^2\cap L^4$$, and the initial temperature is close to a constant in weighted $$L^2$$.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 35B40 Asymptotic behavior of solutions to PDEs 76N15 Gas dynamics (general theory)
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