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Finite element approximation of kinetic dilute polymer models with microscopic cut-off

John W. Barrett, Endre Süli (2011)

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

We construct a Galerkin finite element method for the numerical approximation of weak solutions to a coupled microscopic-macroscopic bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ ℝ d ,d= 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as right-hand side in the momentum equation....

Finite element approximation of kinetic dilute polymer models with microscopic cut-off

John W. Barrett, Endre Süli (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We construct a Galerkin finite element method for the numerical approximation of weak solutions to a coupled microscopic-macroscopic bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ ℝ d , d = 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as right-hand side in the momentum equation....

Fluides incompressibles horizontalement visqueux

Marius Paicu (2003)

Journées équations aux dérivées partielles

Motivé par l'étude des fluides tournants entre deux plaques, nous considérons l'équation tridimensionnelle de Navier-Stokes incompressible avec viscosité verticale nulle. Nous démontrons l'existence locale et l'unicité de la solution dans un espace critique (invariant par le changement d'échelle de l'équation). La solution est globale en temps si la donnée initiale est petite par rapport à la viscosité horizontale. Nous obtenons l'unicité de la solution dans un espace plus grand que l'espace des...

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.

Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases

Marzia Bisi, Laurent Desvillettes (2014)

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

We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in terms of the...

Free Boundary Problems Associated with Multiscale Tumor Models

A. Friedman (2009)

Mathematical Modelling of Natural Phenomena

The present paper introduces a tumor model with two time scales, the time t during which the tumor grows and the cycle time of individual cells. The model also includes the effects of gene mutations on the population density of the tumor cells. The model is formulated as a free boundary problem for a coupled system of elliptic, parabolic and hyperbolic equations within the tumor region, with nonlinear and nonlocal terms. Existence and uniqueness theorems are proved, and properties of the free boundary...

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