DYNAMIC INSTABILITY OF STATIONARY SOLUTIONS TO THE NONLINEAR VLASOV EQUATIONS

Abstract. We present the dynamic instability of smooth compactly supported stationary solu-tions to the nonlinear Vlasov equations with self-consistent attractive forces. For this, we explicitly construct a one-parameter family of perturbed solutions via the method of the Galilean boost. Initially, these perturbations can be close to the given stationary solution as much as possible in any Lp-norm, p ∈ [1,∞], and have the same local mass density profile as a stationary solution, but a different bulk velocity profile. At the macroscopic level, these perturbations correspond to the traveling waves with compact supports. However in finite-time, the phase-space supports of these perturbations will be disjoint from the support of the given stationary solution. This establishes the dynamic instability of stationary solutions in any Lp-norm