论文标题
边界附近剪切流的稳定性
Stability of shear flows near a boundary
论文作者
论文摘要
本书专门研究Navier Stokes方程的剪切流和边界层的线性和非线性稳定性，用于在较小的粘度的情况下，具有差异性边界条件的不可压缩流体。本书的目的是为边界层稳定性的最新进展提供全面的介绍。它针对数学流体动力学的研究生和研究人员，仅假设读者对普通微分方程和复杂分析具有基本知识。流体机械师不需要先决条件，除了包括Leray定理在内的Navier Stokes和Euler方程的基本知识。 这本书由三个部分组成。第一部分致力于呈现经典结果和方法：绿色功能技术，分解技术，分析功能。第二部分的重点是线性分析，首先是瑞利方程，然后是Orr Sommerfeld方程。这样可以为Orr Sommerfeld的绿色功能构建，然后构建线性化Navier Stokes方程的分解。第三部分详细介绍了完整非线性问题和非线性不稳定性结果的近似解决方案的构建。
This book is devoted to the study of the linear and nonlinear stability of shear flows and boundary layers for Navier Stokes equations for incompressible fluids with Dirichlet boundary conditions in the case of small viscosity. The aim of this book is to provide a comprehensive presentation to recent advances on boundary layers stability. It targets graduate students and researchers in mathematical fluid dynamics and only assumes that the readers have a basic knowledge on ordinary differential equations and complex analysis. No prerequisites are required in fluid mechanics, excepted a basic knowledge on Navier Stokes and Euler equations, including Leray's theorem. This book consists of three parts. Part I is devoted to the presentation of classical results and methods: Green functions techniques, resolvent techniques, analytic functions. Part II focuses on the linear analysis, first of Rayleigh equations, then of Orr Sommerfeld equations. This enables the construction of Green functions for Orr Sommerfeld, and then the construction of the resolvent of linearized Navier Stokes equations. Part III details the construction of approximate solutions for the complete nonlinear problem and nonlinear instability results.
