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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/2510.02112 |
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| _version_ | 1866916985654214656 |
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| author | Jeong, In-Jee Tae, Sangwook |
| author_facet | Jeong, In-Jee Tae, Sangwook |
| contents | We consider the Vlasov--Poisson equation on $\mathbb{R}^n \times \mathbb{R}^n$ with $n \ge 3$. We prove local well-posedness in $H^{s}(\mathbb{R}^n \times \mathbb{R}^n)$ with $s> n/2-1/4$, for initial distribution $f_{0} \in H^{s}(\mathbb{R}^n \times \mathbb{R}^n)$ having compact support in $v$. In particular, data not belonging to $L^p(\mathbb{R}^n \times \mathbb{R}^n)$ for large $p$ are allowed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low regularity Sobolev well-posedness for Vlasov--Poisson Jeong, In-Jee Tae, Sangwook Analysis of PDEs We consider the Vlasov--Poisson equation on $\mathbb{R}^n \times \mathbb{R}^n$ with $n \ge 3$. We prove local well-posedness in $H^{s}(\mathbb{R}^n \times \mathbb{R}^n)$ with $s> n/2-1/4$, for initial distribution $f_{0} \in H^{s}(\mathbb{R}^n \times \mathbb{R}^n)$ having compact support in $v$. In particular, data not belonging to $L^p(\mathbb{R}^n \times \mathbb{R}^n)$ for large $p$ are allowed. |
| title | Low regularity Sobolev well-posedness for Vlasov--Poisson |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.02112 |