Finite-time blow-up in the three-dimensional fully parabolic attraction-dominated attraction-repulsion chemotaxis system

Abstract

We show that the attraction-repulsion chemotaxis system{ut=Δu−χ∇⋅(u∇v1)+ξ∇⋅(u∇v2)∂tv1=Δv1−βv1+αu∂tv2=Δv2−δv2+γu, posed with homogeneous Neumann boundary conditions in bounded domains Ω=BR⊂R3, R>0, admits radially symmetric solutions which blow-up in finite time if it is attraction-dominated in the sense that χα−ξγ>0.