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

Xiang FeiYanghai YuMingwen Fei
Oct 2022
摘要
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 modelstarting from $u_0$ is discontinuous at $t = 0$ in the metric of$B^\sigma_{p,\infty}(\R^d)$ with $d\geq1$ and $1\leq p\leq\infty$, whichimplies the ill-posedness for this equation in $B^\sigma_{p,\infty}$. Ourresult 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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