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

We consider the system u t = Δ u − ∇ ⋅ ( χ u ∇ v ) + ∇ ⋅ ( ξ u ∇ w ) , τ v t = Δ v + α u − β v , τ w t = Δ w + γ u − δ w , which has been proposed to describe the aggregation of microglia. We study the problem of global existence and blow-up for this system.