Global boundedness in the higher-dimensional chemotaxis system with indirect signal production and rotational flux

Abstract

We consider a chemotaxis system with indirect signal production and rotational sensitivity: ∂tu=Δu−∇⋅(S(x,u,v,w)⋅∇v)+f(u),(x,t)∈Ω×(0,∞),∂tv=Δv−v+w,(x,t)∈Ω×(0,∞),∂tw=Δw−w+u,(x,t)∈Ω×(0,∞)in a smooth bounded domain Ω⊂RN(N≥2), where S(x,u,v,w)∈RN×N is a matrix-valued function, f is a smooth function and satisfies f(0)≥0 as well as f(s)≤κ−μsα for all s≥0, where κ≥0, μ>0 and α>1. For all sufficiently smooth initial data, we establish the uniqueness and global boundedness of classical solution (u,v,w) in Ω×(0,∞) if α>N4+12.