Solvability of the initial value problem to a model system for water waves (Q493163)

The authors consider the Cauchy problem for a model of water waves. They provide a complete derivation of the model from a Lagrangian formulation introduced by \textit{J. C. Luke} [J. Fluid Mech. 27, 395--397 (1967; Zbl 0146.23701)] and prove global existence of a unique solution for small data. An additional difficulty arises from the fact that the initial hypersurface \(\{t=0\}\) is characteristic.