an:04201725
Zbl 0727.70015
Wan, Yieh-Hei
Nonlinear stability of stationary spherically symmetric models in stellar dynamics
EN
Arch. Ration. Mech. Anal. 112, No. 1, 83-95 (1990).
00174908
1990
j
70F15 85A05
system of particles; Vlasov equation; Poisson law; perturbations; regularity condition; spherically symmetric perturbations
The author considers a system of particles in the three dimensional space without any collision among them. The system can be described by distribution functions f(x,v,t) satisfying the Vlasov equation and the Poisson law. Then \(f_ 0\), for which \(\partial f/\partial t=0\), is nonlinearly stable under some conditions, and is spherically symmetric if \(f(x,v)=f(Sx,Sv)\) with any rotation S.
The author proves that under an appropriate condition of the state \(f_ 0\), \(f_ 0\) is nonlinearly stable subject to general perturbations and that under a regularity condition, \(f_ 0\) is nonlinearly stable subject to spherically symmetric perturbations.
Y.Kozai (Tokyo)