Abstract
First we prove for the equations of a viscous polytropic ideal gas in bounded annular domains in ℝn(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 ℝare asymptotically stable if the initial specific volume is close to a constant in L ∞ and weighted L2, the initial velocity is small in weighted L2 ∩ L4, and the initial temperature is close to a constant in weighted L2.
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Supported by the SFB 256 of the Deutsche Forschungsgemeinschaft at the University of Bonn, the Qidong research grant of the Ministry of Education and the CAEP of China.
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Jiang, S. Large-time behavior of solutions to the equations of a viscous polytropic ideal gas. Annali di Matematica pura ed applicata 175, 253–275 (1998). https://doi.org/10.1007/BF01783686
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DOI: https://doi.org/10.1007/BF01783686