Existence of a Stationary Navier–Stokes Flow Past a Rigid Body, with Application to Starting Problem in Higher Dimensions

We consider the large time behavior of Navier-Stokes flow past a rigid body in $\mathbb{R}^n$ with $n\geq 3$. first construct small stationary solution possessing optimal summability at spatial infinity, which is same as that Oseen fundamental solution. When translational velocity gradually increases and maintained after certain finite time, we then show nonstationary fluid motion converges to corresponding terminal $t\rightarrow\infty$ $L^q$ $q\in[n,\infty]$. This called Finn's starting problem three-dimensional case was affirmatively solved by Galdi, Heywood Shibata $(1997).$ The present paper extends their result higher dimensions. Even for case, our theorem provides new convergence rate, determined infinity seems be sharp.