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March 2008 Shallow water viscous flows for arbitrary topopgraphy
Marc Boutounet, Laurent Chupin, Pascal Noble, Jean Paul Vila
Commun. Math. Sci. 6(1): 29-55 (March 2008).


In this paper, we obtain new models for gravity driven shallow water laminar flows in several space dimensions over a general topography. These models are derived from the incompressible Navier-Stokes equations with no-slip condition at the bottom and include capillary effects. No particular assumption is made on the size of the viscosity and on the variations of the slope. The equations are written for an arbitrary parametrization of the bottom, and an explicit formulation is given in the orthogonal courvilinear coordinates setting and for a particular parametrization so-called “steepest descent” curvilinear coordinates.


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Marc Boutounet. Laurent Chupin. Pascal Noble. Jean Paul Vila. "Shallow water viscous flows for arbitrary topopgraphy." Commun. Math. Sci. 6 (1) 29 - 55, March 2008.


Published: March 2008
First available in Project Euclid: 7 March 2008

zbMATH: 1136.76020
MathSciNet: MR2397996

Primary: 35Q35 , 76B15 , 86A05

Keywords: arbitrary topography , capillary effects , shallow water

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 1 • March 2008
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