Uniform Asymptotic Approximation for Viscous Fluid Flow Down an Inclined Plane.

摘要

An asymptotic method is developed for the linearized Navier-Stokes equations governing the time-dependent motion of a viscous fluid flow down an inclined plane. A diffusion equation for the first order approximation of the fluid surface elevation in a perturbation scheme is derived and a critical Reynolds number is defined based upon the well-posedness of the equation. Under a set of sufficient conditions it is shown that the solution of the diffusion equation is a uniform asymptotic approximation to the generalized solution of the full equations for all time by means of various L2 and pointwise estimates. (Author)