A new Green-Naghdi model in the Camassa-Holm regime and full justification of asymptotic models for the propagation of internal waves

Orateur: TALHOUK Raafat
Localisation: Université libanaise, Liban
Type: Colloque Colette Guillopé
Site: UPEC
Salle: Salle des thèses
Date de début: 13/09/2013 - 11:15
Date de fin: 13/09/2013 - 11:15

This lecture deals with asymptotic models for the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with a flat bottom. We present a new Green-Naghdi type model in the Camassa-Holm (or medium amplitude) regime. This model is fully justified, in the sense that it is consistent, well-posed, and that its solutions remain close to exact solutions of the full Euler system with corresponding initial data. Moreover, our system allows to fully justify any well-posed and consistent lower order model; and in particular the so-called Constantin-Lannes approximation, which extends the classical Korteweg-de Vries equation in the Camassa-Holm regime.