Global existence and blow-up for a system describing the aggregation of microglia

We consider the system ut=Δu−∇⋅(χu∇v)+∇⋅(ξu∇w),τvt=Δv+αu−βv,τwt=Δw+γu−δw, which has been proposed to describe the aggregation of microglia. We study the problem of global existence and blow-up for this system.