Reaction terms avoiding aggregation in slow fluids

We propose a new mathematical model describing the fertilization process of corals and some other invertebrates. As a result we obtain a Keller–Segel system with reaction terms coupled with a Stokes equation. We prove in dimension two that independently of the size of |ρ0|L1|ρ0|L1, there exist global weak solutions. Finally we discuss some open problems arising from our research.