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arXiv · 2210.09859

Ill-posedness of the hyperbolic Keller-Segel model in Besov spaces

Xiang Fei·Yanghai Yu·Mingwen Fei
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Abstract

In this paper, we give a new construction of $u_0\in B^\sigma_{p,\infty}$ such that the corresponding solution to the hyperbolic Keller-Segel model starting from $u_0$ is discontinuous at $t = 0$ in the metric of $B^\sigma_{p,\infty}(\R^d)$ with $d\geq1$ and $1\leq p\leq\infty$, which implies the ill-posedness for this equation in $B^\sigma_{p,\infty}$. Our result generalizes the recent work in \cite{Zhang01} (J. Differ. Equ. 334 (2022)) where the case $d=1$ and $p=2$ was considered.

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Xiang Fei, Yanghai Yu, Mingwen Fei. 2022-10-18. Ill-posedness of the hyperbolic Keller-Segel model in Besov spaces. https://doi.org/10.1007/s00033-023-01952-8

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