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arXiv · 2509.08072

The non-relativistic limit of scattering states for the Vlasov equation with short-range interaction potentials

Younghun Hong·Stephen Pankavich
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Abstract

We study the relativistic and non-relativistic Vlasov equation driven by short-range interaction potentials and identify the large 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 $t \to \infty$. 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 non-relativistic counterparts as $c \to \infty$.

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Younghun Hong, Stephen Pankavich. 2025-09-09. The non-relativistic limit of scattering states for the Vlasov equation with short-range interaction potentials. https://arxiv.org/abs/2509.08072

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