论文标题
在规定的力和扭矩的作用下，在粘性流体中有任意形状的僵硬体的大型行为
Large-Time Behavior of a Rigid Body of Arbitrary Shape in a Viscous Fluid Under the Action of Prescribed Forces and Torques
论文作者
论文摘要
令$ \ Mathcal b $成为一个任意形状的足够光滑的刚体（紧凑型$ \ mathbb r^3 $），在规定的外力的行动下以无限的Navier-Stokes液体移动，$ \ textup {f} $，tormque and torque and torque and tormque，$ \ textup {m} $。我们表明，如果数据适当规则且小，并且$ \ textup {f} $和$ \ textup {m} $在$ l^2 $ - sense中消失了，则至少有一个全球强的解决方案，可以解决相应的初始价值问题。此外，随着时间接近无穷大，该解决方案会收敛为零。到目前为止，只有当$ \ Mathcal b $是一个球时，这种结果才知道。
Let $\mathcal B$ be a sufficiently smooth rigid body (compact set of $\mathbb R^3$) of arbitrary shape moving in an unbounded Navier-Stokes liquid under the action of prescribed external force, $\textup{F}$, and torque, $\textup{M}$. We show that if the data are suitably regular and small, and $\textup{F}$ and $\textup{M}$ vanish for large times in the $L^2$-sense, there exists at least one global strong solution to the corresponding initial-boundary value problem. Moreover, this solution converges to zero as time approaches infinity. This type of results was known, so far, only when $\mathcal B$ is a ball.
