Decay profile for the chemotactic model with advection and quadratic degradation in bounded domains

Abstract

This paper is concerned with a chemotactic system modeling the coral broadcast spawning given by ut+U⋅∇u=Δu−χ∇⋅(u∇v)−μu2,vt+U⋅∇v=Δv−v+u in a bounded domain Ω⊂Rn(n≥1) under Neumann boundary conditions. We provide a rather simpler proof of the non-trivial bounded classical solution on the decay profile. In addition, we also obtain the optimal decay rate of ∇v(⋅,t) in Lp(Ω) as t→∞.