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On the critical mass of the collapse of a gaseous star in spherically symmetric and isentropic motion. (English) Zbl 0913.35108

Summary: For self-gravitating, spherically symmetric and isentropic gaseous star, there is a family of particular solutions when the adiabatic index \(\gamma= 4/3\). We found that there is a critical total mass \(M_0\) associated with these particular solutions. If the total mass \(M\) of the star is less than \(M_0\), then the star expands infinitely and its density ultimately tends to approach zero. When \(M\geq M_0\) and the initial velocity is slower than escape velocity, then the gas is trapped and collapses toward the star’s center in a finite period of time.

MSC:

35Q35 PDEs in connection with fluid mechanics
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
76N15 Gas dynamics (general theory)
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