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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.13592 |
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| _version_ | 1866916009735094272 |
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| author | Luongo, Eliseo Pappalettera, Umberto |
| author_facet | Luongo, Eliseo Pappalettera, Umberto |
| contents | We show that the Cauchy problem associated with the parabolic-elliptic Keller-Segel model is locally ill-posed in $L^q(\mathbb{R}^n)$ for dimensions $n \in \{3,\dots,9\}$ and throughout the supercritical range $q\in [1,\frac{n}{2})$. The non-uniqueness is driven by an instability mechanism in self-similarity variables, in the spirit of the program proposed by Jia and Šverák for the three-dimensional Navier-Stokes equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13592 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral instability and non-uniqueness of mild solutions for the Keller-Segel system Luongo, Eliseo Pappalettera, Umberto Analysis of PDEs Spectral Theory We show that the Cauchy problem associated with the parabolic-elliptic Keller-Segel model is locally ill-posed in $L^q(\mathbb{R}^n)$ for dimensions $n \in \{3,\dots,9\}$ and throughout the supercritical range $q\in [1,\frac{n}{2})$. The non-uniqueness is driven by an instability mechanism in self-similarity variables, in the spirit of the program proposed by Jia and Šverák for the three-dimensional Navier-Stokes equations. |
| title | Spectral instability and non-uniqueness of mild solutions for the Keller-Segel system |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2605.13592 |