论文标题
存在固定的Navier-Stokes的存在流过一个刚体的身体，并应用于更高维度的开始问题
Existence of a Stationary Navier-Stokes Flow Past a Rigid Body, with Application to Starting Problem in Higher Dimensions
论文作者
论文摘要
我们认为，Navier-Stokes的大时间行为流过$ \ Mathbb {r}^n $，带有$ n \ geq 3 $。我们首先构建了具有空间无穷大的最佳总和性的小型固定溶液，该解决方案与Oseen基本解决方案相同。当人体的平移速度逐渐增加并在一定有限的时间后保持维持，然后我们表明，非平稳流体运动会收敛到与人体的小末端速度相对应的固定溶液，作为时间$ t \ rightarrow \ rightarrow \ rightarrow \ rightarrow \ rightarrow \ infty \ rightarrow \ in $ q $ in $ q \ in [n，\ infty] $。这称为芬恩的起始问题，三维案件由加尔迪（Galdi），海伍德（Heywood）和什叶巴塔（Shibata）$（1997）肯定地解决了。$本文将其结果扩展到更高维度的案例。即使在三维情况下，我们的定理也提供了新的收敛速率，这是由无穷大的固定溶液的总结性确定的，并且似乎很清晰。
We consider the large time behavior of the Navier-Stokes flow past a rigid body in $\mathbb{R}^n$ with $n\geq 3$. We first construct a small stationary solution possessing the optimal summability at spatial infinity, which is the same as that of the Oseen fundamental solution. When the translational velocity of the body gradually increases and is maintained after a certain finite time, we then show that the nonstationary fluid motion converges to the stationary solution corresponding to a small terminal velocity of the body as time $t\rightarrow\infty$ in $L^q$ with $q\in[n,\infty]$. This is called Finn's starting problem and the three-dimensional case was affirmatively solved by Galdi, Heywood and Shibata $(1997).$ The present paper extends their result to the case of higher dimensions. Even for the three-dimensional case, our theorem provides new convergence rate, that is determined by the summability of the stationary solution at infinity and seems to be sharp.
