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arXiv · 1304.4554

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

Vincent Duchene·Samer Israwi·Raafat Talhouk
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Abstract

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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Vincent Duchene, Samer Israwi, Raafat Talhouk. 2013-04-16. A new fully justified asymptotic model for the propagation of internal waves in the Camassa-Holm regime. https://doi.org/10.1137/130947064

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