Another Proof of Stability for Global Weak Solutions of 2D Degenerated Shallow Water Models

Abstract

We consider non-linear viscous shallow water models with varying topography, extra friction terms and capillary effects, in a two-dimensional framework. Water-depth dependent laminar and turbulent friction coefficients issued from an asymptotic analysis of the three-dimensional free-surface Navier–Stokes equations are considered here. A new proof of stability for global weak solutions is given in periodic domain Ω = T2, adapting the method introduced by J. Simon in [15] for the non-homogeneous Navier–Stokes equations. Existence results for such solutions can be obtained from this stability analysis.