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Bibliographic Details
Main Authors: Luongo, Eliseo, Pappalettera, Umberto
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.13592
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Table of 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.