| A stellar system can be modelled as an ensemble of mass particles, which attract each other by the Newton's law of attraction. The system can be described by the distribution function satisfying the Vlasov equation and Poisson law. In this paper, we examine the nonlinear stability of the spherically symmetric stationary state f0(∂f 0/∂t = 0) the form of f 0 = &phis;(E0)L l, l > -0.5, where &phis;( E0) = e0- E0m + , and epsilon is contant, 0 < mu < 72 + 4l. i.e. the Emden's model. The Energy-Casimir method is used to establish apriori estimate for the nonlinear stability state for the distribution functions with bounded density functions ‖rho‖ p,l under p,l-norm. We establish the nonlinear stability of Emden's model tinder spherically symmetric perturbations. |
