[hal-00814008] A new fully justified asymptotic model for the propagation of internal waves in the Camassa-Holm regime

This study 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



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