The motion of a fluid-rigid disc system at the zero limit of the rigid disc radius

点涡动力学作为无旋流体中刚体运动的零半径极限

Point vortex dynamics as zero-radius limit of the motion of a rigid body in an irrotational fluid

本文证明点涡动力学可由无旋理想流体中刚体收缩为零半径、固定环量的无质量点粒子时的运动极限得到，并进一步分析了固定质量收缩情形下由 Kutta-Joukowski 型升力控制的二阶极限动力学。

On the motion of a small rigid body in a viscous compressible fluid

We consider the motion of a small rigid object immersed in a viscous compressible fluid in the 3-dimensional Eucleidean space. Assuming the object is a ball of a small radius $\varepsilon$ we show that the behavior of the fluid is not influenced by the object in the asymptotic limit $\varepsilon \to 0$. The result holds for the isentropic pressure law $p(\varrho) = a \varrho^γ$ for any $γ> \frac{3}{2}$ under mild assumptions concerning the rigid body density. In particular, the latter may be bounded as soon as $γ> 3$. The proof uses a new method of construction of the test functions in the wea…

An error bound for the slender body approximation of a thin, rigid fiber sedimenting in Stokes flow

We investigate the motion of a thin rigid body in Stokes flow and the corresponding slender body approximation used to model sedimenting fibers. In particular, we derive a rigorous error bound comparing the rigid slender body approximation to the classical PDE for rigid motion in the case of a closed loop with constant radius. Our main tool is the slender body PDE framework established by the authors and D. Spirn in [18,19], which we adapt to the rigid setting.

关于刚性球簇对粘性流体运动的影响

On the impact of clusters of rigid balls on the motion of a viscous fluid

研究大量刚性球浸没粘性流体的运动问题，提出基于簇概念的新方法，可提高小半径球数量临界值，还能使球在特定极限下随流体流动，即便有引力作用。

Dynamics of several rigid bodies in a two-dimensional ideal fluid and convergence to vortex systems

We consider the motion of several solids in a bounded cavity filled with a perfect incompressible fluid, in two dimensions. The solids move according to Newton's law, under the influence of the fluid's pressure, and the fluid dynamics is driven by the 2D incompressible Euler equations, which are set on the time-dependent domain corresponding to the cavity deprived of the sets occupied by the solids. We assume that the fluid vorticity is initially bounded and that the circulations around the solids may be non-zero. The existence of a unique corresponding solution, à la Yudovich, to this system,…

三维理想不可压缩流中巨型刚性环的运动

Motion of a massive rigid loop in a 3D perfect incompressible flow

本文研究三维无粘不可压缩流体中细长刚性环在半径趋于零时的极限动力学，建立了一阶非线性ODE并识别出类似于二维库塔-茹科夫斯基效应的三维结构，同时刻画了极限流体涡量演化规律。