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

Abstract

In this paper, we first study the local well-posedness for the Cauchy problem of the hyperbolic Keller-Segel equation in Besov spaces Bp,rs(Rd) with 1≤p,r≤+∞ and s>1+dp, 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.