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Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain. (English) Zbl 0858.76069
Summary: We consider the equations of a viscous polytropic ideal gas in the domain exterior to a ball in \(\mathbb{R}^n\) \((n=2\), 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.

MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
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