Large Time existence For 1D Green-Naghdi equations

Samer Israwi (1)

1 IMB - Institut de Mathématiques de Bordeaux

We consider here the $1D $ Green-Naghdi equations that are commonly used in coastal oceanography to describe the propagation of large amplitude surface waves. We show that the solution of the Green-Naghdi equations can be constructed by a standard Picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition.

Mots clés: Green-Naghdi; water-waves; existence

Domaines: Equations aux dérivées partielles [math.AP]

Samer Israwi. Large Time existence For 1D Green-Naghdi equations. 2009. ⟨hal-00415875⟩