Well-posedness and non-uniform dependence for the hyperbolic Keller-Segel equation in the Besov framework.

In this paper, we first study the local well-posedness for the Cauchy problem of the hyperbolic Keller-Segel equation in Besov spaces B p , r s (R d) with 1 ≤ p , r ≤ + ∞ and s > 1 + d p , i.e., the local existence, unique and continuous dependence on the initial data for the solution of this system are obtained, then we further show that this data-to-solution map is not uniformly continuous in these Besov spaces. [ABSTRACT FROM AUTHOR]