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Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

Anatoli Babin, Alex Mahalov, Basil Nicolaenko (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Fast singular oscillating limits of the three-dimensional "primitive" equations of geophysical fluid flows are analyzed. We prove existence on infinite time intervals of regular solutions to the 3D "primitive" Navier-Stokes equations for strong stratification (large stratification parameter N). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear " 2 1 2 dimensional" limit equations...

Feedback stabilization of Navier–Stokes equations

Viorel Barbu (2003)

ESAIM: Control, Optimisation and Calculus of Variations

One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a L Q control problem associated with the linearized equation.

Feedback stabilization of Navier–Stokes equations

Viorel Barbu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a LQ control problem associated with the linearized equation.

Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system

Mehdi Badra (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We study the local exponential stabilization of the 2D and 3D Navier-Stokes equations in a bounded domain, around a given steady-state flow, by means of a boundary control. We look for a control so that the solution to the Navier-Stokes equations be a strong solution. In the 3D case, such solutions may exist if the Dirichlet control satisfies a compatibility condition with the initial condition. In order to determine a feedback law satisfying such a compatibility condition, we consider an extended...

Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system

Mehdi Badra (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We study the local exponential stabilization of the 2D and 3D Navier-Stokes equations in a bounded domain, around a given steady-state flow, by means of a boundary control. We look for a control so that the solution to the Navier-Stokes equations be a strong solution. In the 3D case, such solutions may exist if the Dirichlet control satisfies a compatibility condition with the initial condition. In order to determine a feedback law satisfying such a compatibility condition, we consider an extended...

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...

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