## 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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### References:

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