Other
Scientific paper
May 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997siamj..28..539l&link_type=abstract
SIAM J. Math. Anal., Vol. 28, No. 3, p. 539 - 569
Other
Stellar Models: Stability
Scientific paper
The author studies the linearized stability of stationary solutions of gaseous stars which are in spherically symmetric and isentropic motion. If viscosity is ignored, one has the following three types of problems: (EC), Euler equation with a solid core; (EP), Euler-Poisson equation without a solid core; (EPC), Euler-Poisson equation with a solid core. In Lagrangian formulation, the author proves that any solution of (EC) is neutrally stable. Any solution of (EP) and (EPC) is also neutrally stable when the adiabatic index γ ɛ (4/3,2) and unstable for (EP) when γ ɛ (1,2/3). Moreover, for (EPC) and γ ɛ (1,2), any solution with small total mass is also neutrally stable. When viscosity is present (ν > 0), the velocity disturbance on the outer surface of gas is important. For ν > 0, he proves that the neutrally stable solution (when ν = 0) is now stable with respect to positive-type disturbances, which include Dirichlet and Neumann boundary conditions. The solution can be unstable with respect to disturbances of some other types. The problems were studied through spectral analysis of the linearized operators with singularities at the endpoints of intervals.
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