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Derivation and well-posedness of Boussinesq/Boussinesq systems for internal waves

Cung The Anh (2009)

Annales Polonici Mathematici

We consider the propagation of internal waves at the interface between two layers of immiscrible fluids of different densities, under the rigid lid assumption, with the presence of surface tension and with uneven bottoms. We are interested in the case where the flow has a Boussinesq structure in both the upper and lower fluid domains. Following the global strategy introduced recently by Bona, Lannes and Saut [J. Math. Pures Appl. 89 (2008)], we derive an asymptotic model in this regime, namely the...

Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate

L. Fraštia, U. Thiele, L. M. Pismen (2010)

Mathematical Modelling of Natural Phenomena

We determine the steady-state structures that result from liquid-liquid demixing in a free surface film of binary liquid on a solid substrate. The considered model corresponds to the static limit of the diffuse interface theory describing the phase separation process for a binary liquid (model-H), when supplemented by boundary conditions at the free surface and taking the influence of the solid substrate into account. The resulting variational problem...

Homogenization of a capillary phenomena.

N. Labani, Mongi Mabrouk (1998)

Publicacions Matemàtiques

We study the height of a liquid in a tube when it contains a great number of thin vertical bars and when its border is finely strained. For this, one uses an epi-convergence method.

Numerical study of the Davey-Stewartson system

Christophe Besse, Norbert J. Mauser, Hans Peter Stimming (2004)

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

We deal with numerical analysis and simulations of the Davey-Stewartson equations which model, for example, the evolution of water surface waves. This time dependent PDE system is particularly interesting as a generalization of the 1-d integrable NLS to 2 space dimensions. We use a time splitting spectral method where we give a convergence analysis for the semi-discrete version of the scheme. Numerical results are presented for various blow-up phenomena of the equation, including blowup of defocusing,...

Numerical study of the Davey-Stewartson system

Christophe Besse, Norbert J. Mauser, Hans Peter Stimming (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We deal with numerical analysis and simulations of the Davey-Stewartson equations which model, for example, the evolution of water surface waves. This time dependent PDE system is particularly interesting as a generalization of the 1-d integrable NLS to 2 space dimensions. We use a time splitting spectral method where we give a convergence analysis for the semi-discrete version of the scheme. Numerical results are presented for various blow-up phenomena of the equation, including blowup of defocusing,...

Poche de tourbillon pour Euler 2D incompressible dans un ouvert à bord

Nicolas Depauw (1998)

Journées équations aux dérivées partielles

Nous considérons l'équation d'Euler pour un fluide incompressible dans un domaine borné régulier du plan. Pour une donnée initiale avec un tourbillon de type poche, i.e valant 1 sur un ouvert lisse à bord höldérien et 0 en dehors, nous prouvons l'existence d'une solution de même type, pour tout temps si la poche initiale est décollée du bord du domaine et seulement localement en temps si la poche initiale est tangente au bord. Nous contrôlons l'influence du bord grâce à la théorie des problèmes...

Proof of the double bubble conjecture.

Hutchings, Michael, Morgan, Frank, Ritoré, Manuel, Ros, Antonio (2000)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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