# Zhouping Xin : On Gases Expanding into Vacuum with or without Self-Gravitations

In this talk I will discuss several issues concerning the motions of gases expanding into vacuum with or without self-gravitations which are governed by a free-boundary value problem for the 3-dimnesional compressible Euler system with/or without Poisson equation. A general uniqueness theorem for classical solutions to such a free boundary-value problem is presented for physical vacuums. A typical physical vacuum solution includes the famous Lane-Emdan solution in astrophysics. The uniqueness is proved by a relative entropy argument. Then a local well-posedness theory for spherically symmetric motions is established in a less regular space by a deliberate choice of weighted functional to overcome difficulties arising both at the free surface and the symmetry center. Finally, the uniqueness of the spherically symmetric motions is discussed for general equation of state without self-gravitations. This is a joint work with Professor Tao Luo and Professor Huihui Zeng.

**Category**: Applied Math and Analysis**Duration**: 01:34:51**Date**: April 14, 2014 at 4:25 PM**Views**: 104-
**Tags:**seminar, Applied Math And Analysis Seminar

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