论文标题
稳定的Navier-Stokes在外部结构域中流动的渐近行为
Asymptotic behavior of the steady Navier-Stokes flow in the exterior domain
论文作者
论文摘要
我们考虑了一个椭圆方程，在外部域中具有无界漂移的椭圆方程，并在无穷大时获得定量唯一性估计值，即$ - \ triangle u+w \ cdot \ cdot \ cdot \ cdot \ nabla u = 0 $衰减，以$ \ exp（-c c | x | x | x | x | x | x | x | x | x | x |）的形式衰减。 $ \ | w \ | _ {l^\ infty（\ mathbb {r}^2 \ setMinus b_1）} \ seltsim 1 $，在某些反例的帮助下，它很尖锐。这些结果还概括了整个空间中Kenig-Wang \ cite {KW2015}的衰减定理。作为一种应用，还考虑了不可压缩的流体在有限障碍物周围的渐近行为。特别是对于二维情况，我们可以提高\ cite {kl2019}的衰减速率到$ \ exp（-c | x | x | x | \ log^2 | x | x |）$，其中最小的衰减率（-c c | x | x | x | x | x |^{\ frac32+}）$最近通过kow-caper coite copity in kow-lin cotity in kow-lin copity in 20卡尔曼估计。
We consider an elliptic equation with unbounded drift in an exterior domain, and obtain quantitative uniqueness estimates at infinity, i.e. the non-trivial solution of $-\triangle u+W\cdot\nabla u=0$ decays in the form of $\exp(-C|x|\log^2|x|)$ at infinity provided $\|W\|_{L^\infty(\mathbb{R}^2\setminus B_1)}\lesssim 1$, which is sharp with the help of some counterexamples. These results also generalize the decay theorem by Kenig-Wang \cite{KW2015} in the whole space. As an application, the asymptotic behavior of an incompressible fluid around a bounded obstacle is also considered. Specially for the two-dimensional case, we can improve the decay rate in \cite{KL2019} to $\exp(-C|x|\log^2|x|)$, where the minimal decaying rate of $\exp(-C|x|^{\frac32+})$ is obtained by Kow-Lin in a recent paper \cite{KL2019} by using appropriate Carleman estimates.
