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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.04256 |
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| _version_ | 1866911568653975552 |
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| author | Hong, Younghun Pankavich, Stephen |
| author_facet | Hong, Younghun Pankavich, Stephen |
| contents | We study the long-time asymptotic behavior of small-data solutions to the three-dimensional Vlasov--Riesz system with the inverse power-law potential $λ|x|^{-α}$ in the strictly long-range regime ($0 < α< 1$). By introducing finite- and infinite-time modified wave operators for the characteristic flows, we describe the asymptotic dynamics via convergence to an effective profile along a suitably modified reference flow, and establish modified scattering of solutions. Our proof relies mainly on ODE techniques for the characteristic flows, while also using PDE methods for weighted $W^{1,\infty}$-bounds. Compared with the earlier result (of Huang and Kwon), our Lagrangian approach extends modified scattering to the broader regime $\frac{1}{2}<α<1$ and provides a distinct and more robust argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04256 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modified scattering for the Vlasov-Riesz system with long-range interactions Hong, Younghun Pankavich, Stephen Analysis of PDEs We study the long-time asymptotic behavior of small-data solutions to the three-dimensional Vlasov--Riesz system with the inverse power-law potential $λ|x|^{-α}$ in the strictly long-range regime ($0 < α< 1$). By introducing finite- and infinite-time modified wave operators for the characteristic flows, we describe the asymptotic dynamics via convergence to an effective profile along a suitably modified reference flow, and establish modified scattering of solutions. Our proof relies mainly on ODE techniques for the characteristic flows, while also using PDE methods for weighted $W^{1,\infty}$-bounds. Compared with the earlier result (of Huang and Kwon), our Lagrangian approach extends modified scattering to the broader regime $\frac{1}{2}<α<1$ and provides a distinct and more robust argument. |
| title | Modified scattering for the Vlasov-Riesz system with long-range interactions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.04256 |