论文标题
在高雷诺数（I）的单调剪切流附近的均匀线性触觉阻尼和增强的耗散状态（i）：整个空间案例
Uniform linear inviscid damping and enhanced dissipation near monotonic shear flows in high Reynolds number regime (I): the whole space case
论文作者
论文摘要
我们研究了在$ \ Mathbb {t} \ Times \ Mathbb {r} $上围绕严格单调的剪切流程线性线性的二维Navier Stokes方程的动力学。主要的任务是在自然的假设中了解相关的瑞利和Orr-Sommerfeld方程，即Inviscid情况下单调剪切流周围的线性化操作员没有离散的特征值。我们使用以下视角将非局限性项视为包括小扩散项的主要部分的紧凑型扰动，从而获得了高雷诺数限制中ORR-Sommerfeld方程解决方案的精确控制。作为推论，我们对粘度相对于粘度均匀的Gevrey空间中的线性流动（线性幻影阻尼）中的线性流动提供了详细的描述，并提供了增强的耗散型衰减估计值。关键困难是要准确捕获临界层中ORR-Sommerfeld方程的解决方案的行为。在本文中，我们考虑了$ \ mathbb {t} \ times \ mathbb {r} $上的剪切流的情况。由于边界层的存在，有限通道的情况会带来很大的额外困难，并将在其他地方解决。
We study the dynamics of the two dimensional Navier Stokes equations linearized around a strictly monotonic shear flow on $\mathbb{T}\times\mathbb{R}$. The main task is to understand the associated Rayleigh and Orr-Sommerfeld equations, under the natural assumption that the linearized operator around the monotonic shear flow in the inviscid case has no discrete eigenvalues. We obtain precise control of solutions to the Orr-Sommerfeld equations in the high Reynolds number limit, using the perspective that the nonlocal term can be viewed as a compact perturbation with respect to the main part that includes the small diffusion term. As a corollary, we give a detailed description of the linearized flow in Gevrey spaces (linear inviscid damping) that are uniform with respect to the viscosity, and enhanced dissipation type decay estimates. The key difficulty is to accurately capture the behavior of the solution to Orr-Sommerfeld equations in the critical layer. In this paper we consider the case of shear flows on $\mathbb{T}\times\mathbb{R}$. The case of bounded channels poses significant additional difficulties, due to the presence of boundary layers, and will be addressed elsewhere.
