On measure-preserving selection of solutions of ODEs
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911076226957312 |
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| author | Pappalettera, Umberto |
| author_facet | Pappalettera, Umberto |
| contents | For every $k \in \mathbb{N}$ and $α\in (0,1)$ we construct a divergence-free $u \in C^k([0,T],C^α(\mathbb{T}^d,\mathbb{R}^d))$, $d \geq 2$, such that there is no measurable selection of solutions of the ODE $\dot{X}_t = u(t,X_t)$ that preserves the Lebesgue measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15661 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On measure-preserving selection of solutions of ODEs Pappalettera, Umberto Analysis of PDEs Classical Analysis and ODEs For every $k \in \mathbb{N}$ and $α\in (0,1)$ we construct a divergence-free $u \in C^k([0,T],C^α(\mathbb{T}^d,\mathbb{R}^d))$, $d \geq 2$, such that there is no measurable selection of solutions of the ODE $\dot{X}_t = u(t,X_t)$ that preserves the Lebesgue measure. |
| title | On measure-preserving selection of solutions of ODEs |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2311.15661 |