Global solvability in a three-dimensional cross-diffusion system modeling urban crime propagation

In this paper, we will focus on the no-flux initial-boundary value problem for the three-dimensional cross-diffusion system &u_t=\Delta u-\chi\nabla\cdot(\frac{u}{v}\nabla v)-uv+B_{1}(x,t),& x \in\Omega,t>0, &v_t=\Delta v+uv-v+B_{2}(x,t), & x\in\Omega,t>0 with some positive parameter \chi. Under some basic assumptions on the parameter functions B_{1}, B_{2} and \chi \in (0,\sqrt 3), we show that the system possesses at least one global renormalized solution in case that all model ingredients are radially symmetric with respect to the center of \Omega.