Bresch, Didier; Noble, Pascal Mathematical justification of a shallow water model. (English) Zbl 1158.35401 Methods Appl. Anal. 14, No. 2, 87-117 (2007). Summary: The shallow water equations are widely used to model the flow of a thin layer of fluid submitted to gravity forces. They are usually formally derived from the full incompressible Navier-Stokes equations with free surface under the modeling hypothesis that the pressure is hydrostatic, the flow is laminar, gradually varied and the characteristic fluid height is small relative to the characteristics flow length. This paper deals with the mathematical justification of such asymptotic process assuming a non zero surface tension coefficient and some constraints on the data. We also discuss relation between lubrication models and shallow water systems with no surface tension coefficient necessity. Cited in 20 Documents MSC: 35Q30 Navier-Stokes equations 35R35 Free boundary problems for PDEs 76A20 Thin fluid films 76B45 Capillarity (surface tension) for incompressible inviscid fluids 76D08 Lubrication theory Keywords:Navier-Stokes equations; shallow water; lubrication models; thin domain; free surface; asymptotic analysis; Sobolev spaces PDF BibTeX XML Cite \textit{D. Bresch} and \textit{P. Noble}, Methods Appl. Anal. 14, No. 2, 87--117 (2007; Zbl 1158.35401) Full Text: DOI Euclid OpenURL