標題: Stability of gaseous stars in spherically symmetric motions
作者: Lin, SS
交大名義發表
應用數學系
National Chiao Tung University
Department of Applied Mathematics
關鍵字: stability;isentropic gas;self-gravitating;solid core;limit-point singularity
公開日期: 1-五月-1997
摘要: We study the linearized stability of stationary solutions of gaseous stars which are in spherically symmetric and isentropic motion. If viscosity is ignored, we have 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, we prove that any solution of (EC) is neutrally stable. Any solution of (EP) and (EPC) is also neutrally stable when the adiabatic index gamma is an element of (4/3,2) and unstable for (EP) when gamma is an element of (1, 4/3). Moreover, for (EPC) and gamma is an element of (1, 2), any solution with small total mass is also neutrally stable. When viscosity is present (nu > 0), the velocity disturbance 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 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.
URI: http://hdl.handle.net/11536/567
ISSN: 0036-1410
期刊: SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume: 28
Issue: 3
起始頁: 539
結束頁: 569
顯示於類別:期刊論文


文件中的檔案:

  1. A1997WW98300004.pdf