Mathematical Justification of a Shallow Water Model

Abstract

The shallow water equations are widely used to model the flow of athin layer of fluid submitted to gravity forces. They are usuallyformally derived from the full incompressible Navier-Stokes equationswith free surface under the modeling hypothesis that the pressureis hydrostatic, the flow is laminar, gradually varied and the characteristicfluid height is small relative to the characteristics flow length.This paper deals with the mathematical justification of such asymptoticprocess assuming a non zero surface tension coefficient and someconstraints on the data. We also discuss relation between lubricationmodels and shallow water systems with no surface tension coefficientnecessity.