# American Institute of Mathematical Sciences

February  2001, 1(1): 89-102. doi: 10.3934/dcdsb.2001.1.89

## Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation

 1 INRIA- Project M3N, Rocquencort B.P. 105, F-78153 Le Chesnay Cedex, France, France

Received  November 2000 Revised  January 2001 Published  January 2001

We derive the Saint-Venant system for the shallow waters including small friction, viscosity and Coriolis-Boussinesq factor departing from the Navier-Stokes system with a free moving boundary. This derivation relies on the hydrostatic approximation where we follow the role of viscosity and friction on the bottom. Numerical comparisons between the limiting Saint-Venant system and direct Navier-Stokes simulation allow to validate this derivation.
Citation: Jean-Frédéric Gerbeau, Benoit Perthame. Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 89-102. doi: 10.3934/dcdsb.2001.1.89
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