DYNAMIC INSTABILITY OF THE VLASOV-POISSON-BOLTZMANN SYSTEM IN HIGH DIMENSIONS

We present the existence and dynamic instability of stationary radial solutions to the attractive Vlasov-Poisson-Boltzmann system. We show that all stationary radial solutions are local Maxwellians and for the instability of the stationary radial solution, we explicitly construct a one-parameter family of perturbed solutions via the Galilean boost method. Initially, these perturbed solutions can be close to the given stationary radial solution as much as possible in any L-p-norm, p is an element of (n/2, infinity], n > 2 where n is the spatial dimension. The perturbed solutions have the same local mass density profile as a stationary radial solution but a different bulk velocity profile. At the macroscopic level, these perturbations correspond to traveling waves.