The Nonrelativistic Limit of Scattering States for the Vlasov Equation with Short-Range Interaction Potentials

Abstract. We study the relativistic and nonrelativistic Vlasov equation driven by short-range interaction potentials and identify the long-time dynamics of solutions. In particular, we construct global-in-time solutions launched from small initial data and prove that they scatter along the forward free flow to well-behaved limits as [Formula: see text]. Moreover, we prove the existence of wave operators for such a regime and, upon constructing the aforementioned time asymptotic limits, use the wave operator formulation to prove for the first time that the relativistic scattering states converge to their nonrelativistic counterparts as [Formula: see text].