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

In this paper, we give a new construction of u 0 ∈ B p , ∞ σ 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 p , ∞ σ (R d) with d ≥ 1 and 1 ≤ p ≤ ∞ , which implies the ill-posedness for this equation in B p , ∞ σ . Our result generalizes the recent work in Zhang et al. (J Differ Equ 334:451-489, 2022) where the case d = 1 and p = 2 was considered. [ABSTRACT FROM AUTHOR]