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F -manifolds and integrable systems of hydrodynamic type

Paolo Lorenzoni, Marco Pedroni, Andrea Raimondo (2011)

Archivum Mathematicum

We investigate the role of Hertling-Manin condition on the structure constants of an associative commutative algebra in the theory of integrable systems of hydrodynamic type. In such a framework we introduce the notion of F -manifold with compatible connection generalizing a structure introduced by Manin.

Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants

John W. Barrett, Linda El Alaoui (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a system of degenerate parabolic equations modelling a thin film, consisting of two layers of immiscible Newtonian liquids, on a solid horizontal substrate. In addition, the model includes the presence of insoluble surfactants on both the free liquid-liquid and liquid-air interfaces, and the presence of both attractive and repulsive van der Waals forces in terms of the heights of the two layers. We show that this system formally satisfies a Lyapunov structure, and a second energy...

Finite element discretization of Darcy's equations with pressure dependent porosity

Vivette Girault, François Murat, Abner Salgado (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose...

Finite-dimensional Pullback Attractors for Non-autonomous Newton-Boussinesq Equations in Some Two-dimensional Unbounded Domains

Cung The Anh, Dang Thanh Son (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

We study the existence and long-time behavior of weak solutions to Newton-Boussinesq equations in two-dimensional domains satisfying the Poincaré inequality. We prove the existence of a unique minimal finite-dimensional pullback D σ -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms.

Fluide idéal incompressible en dimension deux autour d’un obstacle fin

Christophe Lacave (2008/2009)

Séminaire Équations aux dérivées partielles

Nous étudions le comportement asymptotique des fluides incompressibles dans les domaines extérieurs, quand l’obstacle devient de plus en plus fin, tendant vers une courbe. Nous étendons les travaux d’Iftimie, Lopes Filho, Nussenzveig Lopes et Kelliher dans lesquels les auteurs considèrent des obstacles se contractant vers un point. En utilisant des outils de l’analyse complexe, nous détaillerons le cas des fluides idéaux en dimension deux autour d’une courbe. Nous donnerons ensuite, à titre indicatif,...

Fluides incompressibles à densité variable

Raphaël Danchin (2002/2003)

Séminaire Équations aux dérivées partielles

 On généralise aux fluides incompressibles à densité variable un certain nombre de résultats bien connus pour les équations de Navier-Stokes et d’Euler incompressibles.

Fluids with anisotropic viscosity

Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher, Emmanuel Grenier (2000)

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

Fluids with anisotropic viscosity

Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher, Emmanuel Grenier (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Motivated by rotating fluids, we study incompressible fluids with anisotropic viscosity. We use anisotropic spaces that enable us to prove existence theorems for less regular initial data than usual. In the case of rotating fluids, in the whole space, we prove Strichartz-type anisotropic, dispersive estimates which allow us to prove global wellposedness for fast enough rotation.

Fokker-Planck equation in bounded domain

Laurent Chupin (2010)

Annales de l’institut Fourier

We study the existence and the uniqueness of a solution  ϕ to the linear Fokker-Planck equation - Δ ϕ + div ( ϕ F ) = f in a bounded domain of  d when F is a “confinement” vector field. This field acting for instance like the inverse of the distance to the boundary. An illustration of the obtained results is given within the framework of fluid mechanics and polymer flows.

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