发表机构
Dalian University of Technology; Taiyuan University of Technology（大连理工大学; 太原理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对二维半空间趋化-Navier-Stokes系统，在滑移边界条件下证明粘性消失极限时边界层解收敛于外层与内层叠加，并给出适定性结果，有助于理解细菌趋化运动。
AI 中文摘要
这是关于二维半空间中耦合趋化-Navier-Stokes系统边界层解的两部分工作的第二部分。在本工作中，我们研究了在二维半平面中，在滑移边界条件下，边界层解关于化学扩散-粘度参数$\varepsilon$（粘性对流系数）的奇异趋化-流体方程的收敛性。更确切地说，我们证明了当$\varepsilon\rightarrow0$时，$\varepsilon>0$的边界层收敛于外层（$\varepsilon=0$时的解）与内层的叠加。外层和内层剖面如第一部分\cite{WWZ}中那样显式推导。此外，附录中给出了耦合趋化-Navier-Stokes系统在余法向Sobolev空间中的适定性结果，这些结果回答了两部分工作中第一部分提出的问题。这项研究有助于理解实验观察到的需氧细菌在流体中向水-空气界面的趋化运动，并丰富了趋化流体模型中边界层的理论结果。
英文摘要
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 $\varepsilon$ in the two-dimensional half-plane. More precisely, we show that the boundary layer for $\varepsilon>0$ (viscous convection coefficient) converges to the superposition of the outer layer (solution with $\varepsilon=0$) and the inner layer as $\varepsilon\rightarrow0$. 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.
