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June 2007 Mathematical Justification of a Shallow Water Model
Didier Bresch, Pascal Noble
Methods Appl. Anal. 14(2): 87-118 (June 2007).


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.


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Didier Bresch. Pascal Noble. "Mathematical Justification of a Shallow Water Model." Methods Appl. Anal. 14 (2) 87 - 118, June 2007.


Published: June 2007
First available in Project Euclid: 7 July 2008

zbMATH: 1158.35401
MathSciNet: MR2437099

Primary: 35Q30, 35R35, 76A20, 76B45, 76D08

Rights: Copyright © 2007 International Press of Boston


Vol.14 • No. 2 • June 2007
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