瑞利問題的初始層

Abstract

In this thesis, we investigate the initial layer for Rayleigh problem of an infinite flat plate set into uniform motion impulsively in its own plane. Rayleigh considered that the fluid is viscous and incompressible and that its motion is governed by the Navier-Stokes equation with the non-slip boundary condition. However, Y.Sone [4] found that the Navier-Stokes equation is not inadequate for the description of the gas shortly after the plane has been set into motion. He investigated the short time behavior of Rayleigh flow with the linearized BKW model equation and obtained the approximation of the flow velocity. We study Rayleigh problem by using the linearized BKW model, the linearized Boltzmann equation and the full Boltzmann equation, respectively. The purpose is to study the gas motion under the diffuse reflection boundary condition. For a small impulsive velocity (small Mach number) and short time, the flow behaves like a free molecule flow. Our analysis is based on certain pointwise estimates for the solution of the problem and flow velocity.