论文标题
通过分解估计值增强了2-D平面Poiseuille流动的耗散和过渡阈值
Enhanced dissipation and transition threshold for the 2-D plane Poiseuille flow via resolvent estimate
论文作者
论文摘要
在本文中，我们研究了具有Navier-Slip边界条件的有限通道中Poiseuille Flow $（1-Y^2,0）$周围2-D Navier-Stokes方程的过渡阈值问题。基于对Poiseuille流的线性化操作员的分解估计值，我们首先建立具有尖锐的衰减速率$ e^{ - c \ c \sqrtνt} $的线性化navier-Stokes方程的增强耗散估计。 As an application, we prove that if the initial perturbation of vortiticy satisfies $$\|ω_0\|_{L^2}\leq c_0ν^{\frac{3}{4}},$$ for some small constant $c_0>0$ independent of the viscosity $ν$, then the solution dose not transition away from the Poiseuille flow for any time.
In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Poiseuille flow $(1-y^2,0)$ in a finite channel with Navier-slip boundary condition. Based on the resolvent estimates for the linearized operator around the Poiseuille flow, we first establish the enhanced dissipation estimates for the linearized Navier-Stokes equations with a sharp decay rate $e^{-c\sqrtνt}$. As an application, we prove that if the initial perturbation of vortiticy satisfies $$\|ω_0\|_{L^2}\leq c_0ν^{\frac{3}{4}},$$ for some small constant $c_0>0$ independent of the viscosity $ν$, then the solution dose not transition away from the Poiseuille flow for any time.
