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Pré-Publication, Document De Travail Année : 2014

An improved result for the full justification of asymptotic models for the propagation of internal waves

Résumé

We consider here asymptotic models that describe 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 uneven bottoms. The aim of this paper is to show that the full justification result of the model obtained by Duchêne, Israwi and Talhouk [to appear in SIAM J. Math. Anal, (arXiv:1304.4554v2)], 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, can be improved in two directions. The first direction is taking into account medium amplitude topography variations and the second direction is allowing strong nonlinearity using a new pseudo-symmetrizer, thus canceling out the smallness assumption of the Camassa-Holm regime for the existence and uniqueness results.
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hal-01094516 , version 1 (12-12-2014)

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Samer Israwi, Ralph Lteif, Raafat Talhouk. An improved result for the full justification of asymptotic models for the propagation of internal waves. 2014. ⟨hal-01094516⟩
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