Scattering of the Vlasov-Riesz system in the three dimensions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916975200960512 |
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| author | Huang, Wenrui Kwon, Hyunwoo |
| author_facet | Huang, Wenrui Kwon, Hyunwoo |
| contents | We consider an asymptotic behavior of solutions to the Vlasov-Riesz system of order $α$ in $\mathbb{R}^3$ which is a kinetic model induced by Riesz interactions. We prove small data scattering when $1/2<α<1$ and modified scattering when $1<α<1+δ$ for some $δ>0$. Moreover, we show the existence of (modified) wave operators for such a regime. To the best of our knowledge, this is the first result on the existence of modified scattering with polynomial correction in kinetic models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scattering of the Vlasov-Riesz system in the three dimensions Huang, Wenrui Kwon, Hyunwoo Analysis of PDEs 35F50, 35Q82, 35B40 We consider an asymptotic behavior of solutions to the Vlasov-Riesz system of order $α$ in $\mathbb{R}^3$ which is a kinetic model induced by Riesz interactions. We prove small data scattering when $1/2<α<1$ and modified scattering when $1<α<1+δ$ for some $δ>0$. Moreover, we show the existence of (modified) wave operators for such a regime. To the best of our knowledge, this is the first result on the existence of modified scattering with polynomial correction in kinetic models. |
| title | Scattering of the Vlasov-Riesz system in the three dimensions |
| topic | Analysis of PDEs 35F50, 35Q82, 35B40 |
| url | https://arxiv.org/abs/2407.16919 |