论文标题
Navier-Stokes方程的COUETTE附近的2D剪切流的稳定性阈值
Stability threshold for 2D shear flows near Couette of the Navier-Stokes equation
论文作者
论文摘要
在本文中，我们考虑了2D剪切流$（y（y），0）^{\ top} $的稳定性阈值。当剪切流与sobolev规范接近couette Flow $（y，0）^{\ top} $在某种意义上，我们在某种意义上证明，如果初始数据$ u_0 $满足$ \ | U_0-（u（y），0），0） $ t \ gg re^{1/3} $的流也接近couette流，为$ t \ to \ infty $。
In this paper, we consider the stability threshold of the 2D shear flow $(U(y),0)^{\top}$ of the Navier-Stokes equation at high Reynolds number $Re$. When the shear flow is near in Sobolev norm to the Couette flow $(y,0)^{\top}$ in some sense, we prove that if the initial data $u_0$ satisfies $\|u_0-(U(y),0)^{\top}\|\leq εRe^{-1/3}$, then the solution of the 2D Navier-Stokes equation approaches to some shear flow which is also close to the Couette flow for $t\gg Re^{1/3}$, as $t\to\infty$.
