标题： 血管模型的层次结构，第二部分：3D-3D 到 3D-1D 和 1D 显示英文标题

标题： A hierarchy of blood vessel models, Part II: 3D-3D to 3D-1D and 1D

摘要： 我们提出并分析了三种模型的血液灌注通过围绕细小动脉或静脉的组织的层次结构。 我们的目标是严格连接3D-3D Darcy--Stokes、3D-1D Darcy--Poiseuille和1D Green's function方法，这些方法常用于模拟此过程。 在第二部分中，我们考虑最详细的一层，即一个3D-3D Darcy-Stokes系统，通过质量守恒和压力/应力平衡条件在可渗透血管表面上耦合。 我们推导出3D-3D模型与第三部分中提出的3D-1D Darcy--Poiseuille模型和1D Green's function模型之间的收敛结果，其速率与$\epsilon^{1/6}|\log\epsilon|$成正比，其中$\epsilon$是最大血管半径。 该速率受到包含一个退化端点的限制，即血管半径消失，即变得无法与毛细血管区分。 我们证明的关键是第I部分中获得的1D积分微分模型的\emph{事前}估计。 显示英文摘要

摘要： We propose and analyze a hierarchy of three models of blood perfusion through a tissue surrounding a thin arteriole or venule. Our goal is to rigorously link 3D-3D Darcy--Stokes, 3D-1D Darcy--Poiseuille, and 1D Green's function methods commonly used to model this process. Here in Part II, we consider the most detailed level, a 3D-3D Darcy-Stokes system coupled across the permeable vessel surface by mass conservation and pressure/stress balance conditions. We derive a convergence result between the 3D-3D model and both the 3D-1D Darcy--Poiseuille model and 1D Green's function model proposed in Part I [Ohm \& Strikwerda, arXiv preprint July 2025] at a rate proportional to $\epsilon^{1/6}|\log\epsilon|$, where $\epsilon$ is the maximum vessel radius. The rate is limited by the inclusion of a degenerate endpoint where the vessel radius vanishes, i.e. becomes indistinguishable from a capillary. Key to our proof are \emph{a priori} estimates for the 1D integrodifferential model obtained in Part I.