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Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2015

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

Résumé

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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Dates et versions

hal-00814008 , version 1 (16-04-2013)
hal-00814008 , version 2 (27-11-2013)
hal-00814008 , version 3 (21-10-2014)

Identifiants

Citer

Vincent Duchene, Samer Israwi, Raafat Talhouk. A new fully justified asymptotic model for the propagation of internal waves in the Camassa-Holm regime. SIAM Journal on Mathematical Analysis, 2015, 47 (1), pp.240-290. ⟨10.1137/130947064⟩. ⟨hal-00814008v3⟩
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