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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.08072 |
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| _version_ | 1866915487412125696 |
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| author | Hong, Younghun Pankavich, Stephen |
| author_facet | Hong, Younghun Pankavich, Stephen |
| contents | 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 $c \to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The non-relativistic limit of scattering states for the Vlasov equation with short-range interaction potentials Hong, Younghun Pankavich, Stephen Analysis of PDEs 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 $c \to \infty$. |
| title | The non-relativistic limit of scattering states for the Vlasov equation with short-range interaction potentials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.08072 |