THE CRITICAL MASS OF COMPRESSIBLE VISCOUS GAS-STARS

Abstract

Let $\gamma $ be the adiabatic index of self-gravitating, spherically symmetric motion of compressible viscous gas-star. When $\gamma \in (1,2]$, we prove the existence of nonisentropic equilibrium. Furthermore, at the adiabatic index $\gamma = \frac {4}{3}$, we found a family of particular solutions which corresponds to an expansive (contractive) gaseous star. Moreover, we find that there is a critical total mass $M_0$. If the total mass $M$ of star is less than $M_0$, then the star expands infinitely. However, if $M \geq M_0$, then there is an ``escape velocity'' $v_er$ associated with $M$ and the initial configuration of the star. If $v(0,r) \geq v_er$, then the star will expand infinitely. If $v(0,r) \lt v_er$, then it will collapse after a finite time.