Global solutions and stability for self-gravitating isentropic gases
The author considers the system \[ {\partial\over\partial t}\rho+ {\partial\over \partial r}(\rho u)+{2\over r}\rho u=0, \] \[ {\partial\over \partial t}(\rho u)+{\partial \over\partial r} (\rho u^2+p)+ {2\over r}\rho u^2= -{\rho\over r^2}\left[ r+g\int^r_{R_0} \rho(s,t)s^2 ds\right], \] \(r>R_0>0\), \(p= {\rho^\gamma\over\gamma}\), \(\gamma\in(0,2)\), with initial-boundary condition. He constructs approximate solutions and provides stability, convergence and consistency results.
scientific article; zbMATH DE number 1251430