We exploit a two-dimensional model (Ghosh et al. in Q J Mech Appl Math 71(3):349–367, 2018; Kozlov and Nazarov in Dokl Phys 56(11):560–566, 2011, J Math Sci 207(2):249–269, 2015) describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic flows in an infinite cylinder with such intricate boundary conditions. The main result is that solutions of this problem do not depend on the period and they are nothing else but the time independent Poiseuille flow. Similar solutions of the Stokes equations for the rigid wall (the no-slip boundary condition) depend on the period and their profile depends on time.

我们利用二维模型（Ghosh 等人在 QJ Mech Appl Math 71(3):349–367, 2018 中；Kozlov 和 Nazarov 在 Dokl Phys 56(11):560–566, 2011 中，J Math Sci 207（ 2):249–269, 2015) 描述了考虑与周围肌肉组织和 3D 流体流动的相互作用的柔性血管壁的弹性行为。我们研究具有如此复杂边界条件的无限圆柱体中的时间周期流动。主要结果是这个问题的解决方案不依赖于周期，它们只是与时间无关的泊肃叶流。刚性壁（无滑移边界条件）的斯托克斯方程的类似解取决于周期，它们的轮廓取决于时间。