Boundary layer analysis for the 2D Chemotaxis-Navier-Stokes system with logarithmic sensitivity, Part II. viscous vanishing limit
Abstract
This is the second part of a two-part work concerning boundary layer solutions to the coupled Chemotaxis-Navier-Stokes system in the two-dimensional half-space. In the present work, we address the convergence of boundary layer solutions to singular chemotaxis-fluid equations under slip boundary conditions with respect to the chemical diffusion-viscosity parameter ε in the two-dimensional half-plane. More precisely, we show that the boundary layer for ε>0 (viscous convection coefficient) converges to the superposition of the outer layer (solution with ε=0) and the inner layer as ε→0. The outer and inner profiles are explicitly derived as in the first part\cite{WWZ}. Furthermore, the well-posedness results of the coupled Chemotaxis-Navier-Stokes system in conormal Sobolev spaces will be presented in Appendix. They answer the question mentioned in the first part of the two-part work. This study could help the understanding of the chemotactic movement of aerobic bacteria to the water-air surface observed experimentally in fluids, and enrich the theoretical results of boundary layer in chemotactic fluid models.
Related
- Convergence rates in the periodic homogenization of vanishing-viscous Hamilton-Jacobi equations
- A logarithmic Bogomolov--Sommese vanishing theorem on compact Kähler manifolds
- Global solvability with arbitrary mass for a chemotaxis--fluid model with sensitivity growth between linear and quadratic
- Local null controllability of a parabolic-elliptic chemotaxis system by a Neumann boundary control
- Boundedness in a chemotaxis system with nonlinear diffusion and singular sensitivity
BibTeX
@misc{wang2026boundary,
title = {{Boundary layer analysis for the 2D Chemotaxis-Navier-Stokes system with logarithmic sensitivity, Part II. viscous vanishing limit}},
author = {Hui Wang and Lingling Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11027},
eprint = {2609.11027},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11027},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Boundary layer analysis for the 2D Chemotaxis-Navier-Stokes system with logarithmic sensitivity, Part II. viscous vanishing limit
AU - Hui Wang
AU - Lingling Zhao
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.11027
UR - https://arxiv.org/abs/2609.11027
AB - This is the second part of a two-part work concerning boundary layer solutions to the coupled Chemotaxis-Navier-Stokes system in the two-dimensional half-space. In the present work, we address the convergence of boundary layer solutions to singular chemotaxis-fluid equations under slip boundary conditions with respect to the chemical diffusion-viscosity parameter ε in the two-dimensional half-plane. More precisely, we show that the boundary layer for ε>0 (viscous convection coefficient) converges to the superposition of the outer layer (solution with ε=0) and the inner layer as ε→0. The outer and inner profiles are explicitly derived as in the first part\cite{WWZ}. Furthermore, the well-posedness results of the coupled Chemotaxis-Navier-Stokes system in conormal Sobolev spaces will be presented in Appendix. They answer the question mentioned in the first part of the two-part work. This study could help the understanding of the chemotactic movement of aerobic bacteria to the water-air surface observed experimentally in fluids, and enrich the theoretical results of boundary layer in chemotactic fluid models.
ER -