Display Abstract
 Title On the thin film approximation for the flow of a viscous incompressible fluid down an inclined plane
 Name Hiroki Ueno Country Japan Email mathematics@a7.keio.jp Co-Author(s) Tatsuo Iguchi and Akinori Shiraishi Submit Time 2014-02-25 06:21:14 Session Special Session 37: Global or/and blowup solutions for nonlinear evolution equations and their applications
 Contents We consider two-dimensional motion of liquid film of a viscous incompressible fluid down an inclined plane in the influence of the gravity and the surface tension. In order to investigate such a motion, a method of the thin film approximation is often used. It is the approximation by the perturbation expansion of the solution for the nondimensional parameter $\delta$ defined by ratio between the thickness of the liquid film and the typical wave length. In this study, we will give uniform estimates of the solution to the original Navier--Stokes equations in $\delta$ when the Reynolds number, the angle of inclination, and the initial date are sufficiently small.