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Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain

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Abstract

We consider the equations of a viscous polytropic ideal gas in the domain exterior to a ball in ℝn (n=2 or 3) and prove the global existence of spherically symmetric smooth solutions for (large) initial data with spherical symmetry. The large-time behavior of the solutions is also discussed. To prove the existence we first study an approximate problem in a bounded annular domain and then obtain a priori estimates independent of the boundedness of the annular domain. Letting the diameter of the annular domain tend to infinity, we get a global spherically symmetric solution as the limit.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse 10, D-53115, Bonn, Germany

    Song Jiang

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  1. Song Jiang
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Additional information

Communicated by H. Araki

Dedicated to Professor Rolf Leis on the occasion of his 65th birthday

Supported by the SFB 256 of the Deutsche Forschungsgemeinschaft at the University of Boon.

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Jiang, S. Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain. Commun.Math. Phys. 178, 339–374 (1996). https://doi.org/10.1007/BF02099452

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  • DOI: https://doi.org/10.1007/BF02099452

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