Global weak solutions for a two-species Riesz cross-attraction system with quadratic diffusion

We establish global existence for a two-species cross-attraction system on $\mathbb R^3$, with quadratic diffusion and the common interaction operator $(-Δ)^{-s}$, where $1/2<s<1$. Nonnegative initial data in $L^1\cap L^\infty$ with finite second moments require no smallness condition on the masses.