We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space ${\mathbb{R}}^3$. The motion of the fluid is modeled by the Navier–Stokes equations, whereas the motion of the rigid body is described by the conservation law of linear and angular momentum. Under the assumption that the diameter of the rigid body tends to zero and that the density of the rigid body goes to infinity, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier–Stokes equations in the full space without rigid body.

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关于 3D 不可压缩流动中的小刚体极限

我们考虑一个小的刚体在充满整个空间的不可压缩粘性流体中的演化 ${\mathbb{电阻}}^3$. 流体的运动由纳维-斯托克斯方程建模，而刚体的运动由线性和角动量守恒定律描述。在刚体直径趋于零且刚体密度趋于无穷大的假设下，我们证明流体刚体系统的解收敛到纳维-斯托克斯方程的全解没有刚体的空间。