AI 中文总结
本文研究三维粘性流体中浸入的小刚体与流体耦合系统，证明当刚体尺寸和流体粘性消失时，极限速度场由全空间不可压缩欧拉方程支配，流体对刚体运动的影响在该极限下消失。
AI 中文摘要
本文研究三维不可压缩粘性流体中浸入的刚体所构成的流固耦合系统，当刚体尺寸与流体粘性均消失时的渐近行为。我们证明，极限速度场由全空间不可压缩欧拉方程支配，且该极限下流体对刚体运动的影响消失。
英文摘要
In this paper, we investigate the asymptotic behavior of a coupled fluid--rigid body system, consisting of a rigid body immersed in a three-dimensional viscous incompressible fluid, as the body size and the fluid viscosity vanish. We prove that the limiting velocity field is governed by the whole-space incompressible Euler equations. Moreover, the influence of the fluid on the rigid body motion is shown to vanish in this limit.
