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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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