游动细丝弹性流体力学的适定性及其应用
Well-posedness and applications of classical elastohydrodynamics for a swimming filament
摘要：
我们考虑一个经典的弹性流体动力学模型的不可伸展的细丝进行平面运动在$\mathbb{R}^3$。流体力学由阻力理论描述，纤维弹性由欧拉-伯努利梁理论控制。我们的目标是双重的：（1）作为发展细丝弹性流体动力学的数学分析的起点，特别是不可伸展性约束的分析处理，和（2）作为应用，证明允许自由端细丝游动的内部纤维强迫条件。我们的纤维游泳速度的分析补充了内部纤维强迫的数值优化，以及一种新的数值方法模拟不可伸展的游泳者。
英文摘要：
We consider a classical elastohydrodynamic model of an inextensible filament undergoing planar motion in $\mathbb{R}^3$. The hydrodynamics are described by resistive force theory, and the fiber elasticity is governed by Euler-Bernoulli beam theory. Our aim is twofold: (1) Serve as a starting point for developing the mathematical analysis of filament elastohydrodynamics, particularly the analytical treatment of an inextensibility constraint, and (2) As an application, prove conditions on internal fiber forcing that allow a free-ended filament to swim. Our analysis of fiber swimming speed is supplemented with a numerical optimization of the internal fiber forcing, as well as a novel numerical method for simulating an inextensible swimmer.
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