Study On The Stability Of Three-dimensional Dynamic Equilibrium State Of Self-weight Vlasov-Poisson Gas

This paper is devoted to the study of the stability of three–dimensional states of dynamic equilibrium of self–gravitating Vlasov–Poisson gas.In order to prove absolute instability of spatial dynamic equilibrium states of Vlasov–Poisson gas with respect to small three–dimensional(3D)perturbations,transition from kinetic equations to infinite system of gas–dynamic equations of the “vortex shallow water” type in Boussinesq approximation is completed by Zakharov replacement of variables.In this paper,sufficient condition for stability of exact stationary solutions to equations of hydrodynamic type relative to small spatial perturbations is established.Well–known sufficient Newcomb–Gardner–Rosenbluth condition for linear stability is reversed.The basic differential inequality is obtained.From this inequality,a priori exponential lower estimate for the growth of small 3D perturbations is derived when sufficient conditions for practical linear instability are executed.Absolute linear instability of the studied spatial dynamic equilibrium states of Vlasov–Poisson gas relative to small 3D perturbations is proven.Formal nature of Newcomb–Gardner–Rosenbluth condition is discovered.The established results spread classical Earnshaw theorem from analytical mechanics to statistical one.Using the results obtained,it is possible to study mathematical models of gas for adequacy to the physical phenomena described by them.