A note on the well-posedness of the one-dimensional multilayer shallow water model

Vincent Duchêne (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this short note, we prove by elementary means that the one-dimensional multilayer shallow-water (or Saint-Venant) model for density-stratified fluids is well-posed, provided that (i) the density stratification is stable (i.e. the denser fluid is deeper); (ii) each layer has non-vanishing depth; (iii) the shear velocities are small enough.

Mots clés: multilayer shallow-water; hyperbolicity

Domaines: Equations aux dérivées partielles [math.AP]

Vincent Duchêne. A note on the well-posedness of the one-dimensional multilayer shallow water model. 2013. ⟨hal-00922045⟩