论文标题
在粘性流体中二维COUETTE流的渐近稳定性
Asymptotic stability of two-dimensional Couette flow in a viscous fluid
论文作者
论文摘要
在本文中，我们研究了COUETTE FLOW的非线性渐近稳定性，用于二维Navier-Stokes方程，带有较小的粘度$ν> 0 $ in $ \ MATHBB {T} \ times \ times \ times \ Mathbb {r} $。普遍知道，COUETTE流的非线性渐近稳定性紧密取决于初始扰动的大小和规律性，这产生了稳定性阈值问题。这项工作研究了使非线性渐近稳定性成立的初始扰动的大小和规则性之间的关系。更准确地说，我们证明了，如果初始扰动在某些gevrey-$ \ frac {1} {s} $ class，size $ $ s \ geq \ geq \ geq \ frac {1-3β} {1-3β} {1-3β} {2-3β} $持有。
In this paper, we study the nonlinear asymptotic stability of Couette flow for the two-dimensional Navier-Stokes equation with small viscosity $ν>0$ in $\mathbb{T}\times\mathbb{R}$. It's generally known the nonlinear asymptotic stability of the Couette flow depends closely on the size and regularity of the initial perturbation, which yields the stability threshold problem. This work studies the relationship between the size and the regularity of the initial perturbation that makes the nonlinear asymptotic stability holds. More precisely, we proved that if the initial perturbation is in some Gevrey-$\frac{1}{s}$ class with size $εν^β$ where $s\geq \frac{1-3β}{2-3β}$ and $β\in [0,\frac{1}{3}]$, then the nonlinear asymptotic stability holds.
