Boussinesq/Boussinesq systems for internal waves with a free surface, and the KdV approximation

Vincent Duchêne

Displaying similar documents to “Boussinesq/Boussinesq systems for internal waves with a free surface, and the KdV approximation”

Long-Wave Coupled Marangoni - Rayleigh Instability in a Binary Liquid Layer in the Presence of the Soret Effect

A. Podolny, A. A. Nepomnyashchy, A. Oron (2008)

Mathematical Modelling of Natural Phenomena

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We have explored the combined long-wave Marangoni and Rayleigh instability of the quiescent state of a binary- liquid layer heated from below or from above in the presence of the Soret effect. We found that in the case of small Biot numbers there are two long- wave regions of interest ~ and ~ . The dependence of both monotonic and oscillatory thresholds of instability in these regions on both the Soret and dynamic Bond numbers has been investigated....

Initial-boundary value problems for second order systems of partial differential equations

Heinz-Otto Kreiss, Omar E. Ortiz, N. Anders Petersson (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of equations as a larger first order system. Unfortunately, the resulting first order system consists, in general, of more than 2 equations which leads to many complications, such as side conditions which must be satisfied by the solution of the larger...

Two shallow-water type models for viscoelastic flows from kinetic theory for polymers solutions

Gladys Narbona-Reina, Didier Bresch (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this work, depending on the relation between the Deborah, the Reynolds and the aspect ratio numbers, we formally derived shallow-water type systems starting from a micro-macro description for non-Newtonian fluids in a thin domain governed by an elastic dumbbell type model with a slip boundary condition at the bottom. The result has been announced by the authors in [G. Narbona-Reina, D. Bresch, Springer Verlag (2010)] and in the present paper, we provide a self-contained description,...

Asymptotic-Preserving scheme for a two-fluid Euler-Lorentz model

Stéphane Brull, Pierre Degond, Fabrice Deluzet, Alexandre Mouton (2011)

ESAIM: Proceedings

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The present work is devoted to the simulation of a strongly magnetized plasma as a mixture of an ion fluid and an electron fluid. For simplicity reasons, we assume that each fluid is isothermal and is modelized by Euler equations coupled with a term representing the Lorentz force, and we assume that both Euler systems are coupled through a quasi-neutrality constraint of the form = . The numerical...

T-coercivity for scalar interface problems between dielectrics and metamaterials

Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Patrick Ciarlet (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipation is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of R, with = 23. Our aim is to characterize occurences where the problem is well-posed within the Fredholm (or...