Displaying similar documents to “Derivation and well-posedness of Boussinesq/Boussinesq systems for internal waves”

Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves

David Lannes (2008-2009)

Séminaire Équations aux dérivées partielles

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This note is devoted to the study of a bi-fluid generalization of the nonlinear shallow-water equations. It describes the evolution of the interface between two fluids of different densities. In the case of a two-dimensional interface, this systems contains unexpected nonlocal terms (that are of course not present in the usual one-fluid shallow water equations). We show here how to derive this systems from the two-fluid Euler equations and then show that it is locally well-posed. ...

Asymptotic analysis of surface waves due to high-frequency disturbances

Nikolay Kuznetsov, Vladimir Gilelevich Maz'ya (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The present paper is devoted to the asymptotic analysis of the linear unsteady surface waves. We study two problems concerned with high-frequency surface and submerged disturbances. The two-scale asymptotic series are obtained for the velocity potential. The principal terms in the asymptotics of some hydrodynamical characteristics of the wave motion (the free surface elevation, the energy, etc.) are described.