納維-斯托克斯方程，以克勞德-路易-納維和喬治-斯托克斯命名，是一組描述流體物質的方程組。他們是最有用的方程組之一，因為它描述了許多物理上以及工程上有趣的現象。它們可以用於模擬大氣、洋流、管道中的水流以及翼型周圍的氣流等等。它們的完整版以及簡化版都可以幫助飛行器和汽車的設計、血液循環的研究、發電廠的設計、污染分析以及許多其他用途。在純數學理論的研究上，納維-斯托克斯方程也引起了許多數學家的注意。

在這篇論文中，我們會對[11] 關於不可壓縮流體在有界障礙物以外的漸進行為的結果進行改進。在比起[11] 更少的假設下，任何非零速度場都有最小衰減率 exp(-C|x|^(3/2) log|x|)。我們的證明使用了適當的卡爾曼估計以及規律性結果，也就是不含時納維-斯托克斯方程的肖德估計。

The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances. Navier-Stokes equations are useful because they describe the physics of many phenomena of scientific and engineering interest. They may be used to model the weather, ocean currents, water flow in a pipe and air flow around a wing. The Navier-Stokes equations in their full and simplified forms help with the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of pollution, and many other things. The Navier-Stokes equations are also of great interest in a purely mathematical sense.

In this thesis we improve the result in [11], which concern about the asymptotic behavior of an incompressible fluid around a bounded obstacle. Under some assumptions weaker than [11], any nontrivial velocity field obeys a minimal decaying rate exp(-C|x|^(3/2) log|x|) at infinity. Our proof is based on appropriate Carleman estimates and the regularity result, namely the Schauder's Estimate for stationary Navier-Stokes
equation.

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