Global boundedness in a chemotaxis system with signal-dependent motility and indirect signal consumption

Abstract

This paper deals with the following chemotaxis system ut=Δuγv,x∈Ω,t>0,vt=Δv−vw,x∈Ω,t>0,wt=−δw+u,x∈Ω,t>0,under homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂Rn (n≤3), where the motility function γ∈C30,+∞ is positive on [0,∞). For all suitably regular initial data, then the corresponding initial boundary value problem possesses a unique global classical solution which is uniformly bounded. The purpose of this work is to remove the smallness assumption on ‖v0‖L∞(Ω) in three dimension (Xu et al., 0000).