LINEAR-STABILITY OF STATIONARY SOLUTIONS OF THE VLASOV-POISSON SYSTEMIN 3 DIMENSIONS

Rigorous results on the stability of stationary solutions of the Vlaso v-Poisson system are obtained in the contexts of both plasma physics a nd stellar dynamics. It is proved that stationary solutions in the pla sma physics (stellar dynamics) case are linearly stable if they are de creasing (increasing) functions of the local, i.e., particle, energy. The main tool in the analysis is the free energy, a conserved quantity of the linearized system. In addition, an appropriate global existenc e result is proved for the linearized Vlasov-Poisson system and the ex istence of stationary solutions which satisfy the above stability cond ition is established.