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.
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Communicated by O. Pironneau
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Fabrie, P., Marche, F. Another Proof of Stability for Global Weak Solutions of 2D Degenerated Shallow Water Models. J. Math. Fluid Mech. 11, 536 (2009). https://doi.org/10.1007/s00021-008-0271-4
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DOI: https://doi.org/10.1007/s00021-008-0271-4