Boundary layer problem on chemotaxis-Navier-Stokes system with Robin boundary conditions

2022/05/17 by Qianqian Hou, Hou, Qianqian
Mathematics · #35A01 #35B40 #35B44 #35K57 #35Q92 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2205.08049

openalex publication_date 2022/05/17 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the boundary layer problem on a chemotaxis-Navier-Stokes system modelling boundary layer formation of aerobic bacteria in fluid. Completing the system with physical Robin-type boundary conditions for oxygen, no-flux and Dirichlet boundary conditions for bacteria and fluid velocity, we show that the gradients of its radial solutions in a region between two concentric spheres possessing boundary layer effects as the oxygen diffusion rate ε goes to zero and the boundary-layer thickness is of order O(ε^α) with 0

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