The Green-Naghdi model is currently the most well-known model used for numerical simulations of waterfront streams, even in setups that incorporate vanishing depth (at the shoreline) and wave breaking. Regardless of their many favorable circumstances, the Green-Naghdi equations specially take into consideration neglected rotational effects, which are significant for wind-driven waves, waves riding upon a sheared current, waves near a ship, or tsunami waves approaching a shore. The Green-Naghdi system is first rewritten as an equivalent system by using an adequate change of unknowns. We show that solutions to the model here considered, with voracity and surface tension, may be obtained by a standard Picard iterative scheme. No loss of regularity is involved with respect to the initial data. Moreover solutions exist at the same level of regularity as for 1st order hyperbolic symmetric systems, i.e. with a regularity in...

more