Boundary layer effects induced by the fluid in a chemotaxis-Navier-Stokes system

Abstract

This paper is concerned with the boundary layer problem on a chemotaxis-Navier-Stokes system modelling the boundary layer formation of aerobic bacteria in fluids. Completing this system with Neumann boundary conditions on oxygen, we show that gradients of its second solution component in the half plane of $\mathbb{R}^2$ possess boundary layer effects as the oxygen diffusion rate goes to zero. However, neglecting the influence of the fluid, gradients of solutions to the chemotaxis-only subsystem no longer present such boundary layer effects. It seems that the boundary layer effect for the chemotaxis-Navier-Stokes system under Neumann boundary conditions on oxygen is induced by the presence of fluids.45