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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 ⊂ ,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....
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 ⊂ , 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....
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...
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.
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...
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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