论文标题
关于粘性不可压缩的流体中大量小刚体的运动
On the motion of a large number of small rigid bodies in a viscous incompressible fluid
论文作者
论文摘要
我们考虑$ n $刚体的运动 - 紧凑集$（\ Mathcal {s}^1_ \ Varepsilon，\ cdots，\ Mathcal {s}^n_ \ varepsilon）_ {\ varepsilon> 0} 在Euclidean Space $ \ Mathbb {r}^d $，$ d = 2,3 $中包含在域中的域中。 我们显示流体流不受渐近极限$ \ varepsilon \ to 0 $和$ n = n（\ varepsilon）\ rightarrow \ rightarrow \ rightarrow \ rightarrow \ infty $的影响不受无限多体的存在的影响。 立刻 \ [ {\ rm diam} [\ Mathcal {s}^i_ \ varepsilon] \至0 \ \ mbox {as} \ \ varepsilon \ to 0，\ i = 1，\ cdots，n（\ varepsilon）。 \] 结果仅取决于身体的几何形状，与它们的质量密度无关。允许使用有限的能量进行冲突，并且初始数据是任意的。
We consider the motion of $N$ rigid bodies -- compact sets $(\mathcal{S}^1_\varepsilon, \cdots, \mathcal{S}^N_\varepsilon )_{\varepsilon > 0}$ -- immersed in a viscous incompressible fluid contained in a domain in the Euclidean space $\mathbb{R}^d$, $d=2,3$. We show the fluid flow is not influenced by the presence of the infinitely many bodies in the asymptotic limit $\varepsilon \to 0$ and $N=N(\varepsilon)\rightarrow\infty$ as soon as \[ {\rm diam}[\mathcal{S}^i_\varepsilon ] \to 0 \ \mbox{as}\ \varepsilon \to 0 ,\ i=1,\cdots, N(\varepsilon). \] The result depends solely on the geometry of the bodies and is independent of their mass densities. Collisions are allowed and the initial data are arbitrary with finite energy.
