Recent mathematical results and open problems about shallow water equations. Analysis and simulation of fluid dynamic

Didier Bresch (1, 2) , Benoît Desjardins (3) , Guy Metivier (4)

1 LAMA - Laboratoire de Mathématiques
2 LMC - IMAG - Laboratoire de Modélisation et Calcul
3 ENS-PSL - École normale supérieure - Paris
4 IMB - Institut de Mathématiques de Bordeaux

The purpose of this work is to present recent mathematical results about the shallow water model. We will also mention related open problems of high mathematical interest.

Mots clés: Viscous and inviscid flow; shallow-water model; lake equations; quasi-geostrophic equations; weak and strong solutions; degenerate viscosities

Domaines: Equations aux dérivées partielles [math.AP]

Didier Bresch, Benoît Desjardins, Guy Metivier. Recent mathematical results and open problems about shallow water equations. Analysis and simulation of fluid dynamic. Analysis and Simulation of Fluid Dynamics, Birkhäuser, pp.15-31, 2007, ⟨10.1007/978-3-7643-7742-7_2⟩. ⟨hal-00385916⟩