The Existence of Weak Solutions for Bidirectional Fluid–Structure Coupling Problem in 2D Arterial Blood Flow

In this paper, we study a two-dimensional (2D) bidirectional fluid–solid coupling problem in blood vessels and prove the existence of weak solutions to this kind of problem. When studying the fluid motion of arterial blood flow in arterial vascular tissue, where the density of the vessel wall is roughly equal to that of the blood, the coupling between the blood and the vessel wall is highly nonlinear. In this case, the fluid space where the arterial blood flow is located is no longer fixed in the fluid–structure interaction (FSI) model, and its boundary position is determined by the position of the elastic vessel wall. The contact force exerted by the elastic vascular structure on the blood flow also affects the movement of the blood flow, while the position of the blood vessel is determined by the contact force exerted by the blood flow on the blood vessel; that is, two-way coupling occurs between the vascular diameter and the blood flow space.MSC2020 Classification: 35D30, 35M31