STABILITY OF GASEOUS STARS IN SPHERICALLY SYMMETRICAL MOTIONS

We study the linearized stability of stationary solutions of gaseous s tars which are in spherically symmetric and isentropic motion. If visc osity is ignored, we have following three types of problems: (EC), Eul er equation with a solid core; (EP), Euler-Poisson equation without a solid core; (EPC), Euler-Poisson equation with a solid core. In Lagran gian formulation, we prove that any solution of (EC) is neutrally stab le. Any solution of (EP) and (EPC) is also neutrally stable when the a diabatic index gamma is an element of (4/3,2) and unstable for (EP) wh en gamma is an element of (1, 4/3). Moreover, for (EPC) and gamma is a n element of (1, 2), any solution with small total mass is also neutra lly stable. When viscosity is present (nu > 0), the velocity disturban ce on the outer surface of gas is important. For nu > 0, we prove that the neutrally stable solution (when nu = 0) is now stable with respec t to positive-type disturbances, which include Dirichlet and Neumann b oundary conditions. The solution can be unstable with respect to distu rbances of some other types. The problems were studied through spectra l analysis of the linearized operators with singularities at the endpo ints of intervals.