Well-posedness and non-uniform dependence for the hyperbolic Keller-Segel equation in the Besov framework (Q2232198)

The, so-called, hyperbolic Keller-Segel model of chemotaxis \[ u_t+\nabla\cdot(u(1-u)\nabla S)=0, \] \[\Delta S=S-u, \] is studied in the whole space \(\mathbb{R}^d\). Local-in-time well-posedness of the Cauchy problem is established in suitable Besov spaces. A nonuniform continuity property of the data-to-solution map is shown.