Addition au Mémoire sur la Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire, etc.
Blow-up in a modified Constantin-Lax-Majda model for the vorticity equation.
Einige Betrachtungen über die Gleichungen der Hydrodynamik
Interaction des tourbillons dans les écoulements plans faiblement visqueux
Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain
We study the long-time behavior of infinite-energy solutions to the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. The initial data we consider are finite-energy perturbations of a smooth vortex with small circulation at infinity, but are otherwise arbitrarily large. Using a logarithmic energy estimate and some interpolation arguments, we prove that the solution approaches a self-similar Oseen vortex as . This result was obtained in...
Persistance de structures géométriques et limite non visqueuse pour les fluides incompressibles en dimension quelconque
Poches de tourbillon singulières dans un fluide faiblement visqueux.
In this paper, we study the singular vortex patches in the two-dimensional incompressible Navier-Stokes equations. We show, in particular, that if the initial vortex patch is C1+s outside a singular set Σ, so the velocity is, for all time, lipschitzian outside the image of Σ through the viscous flow. In addition, the correponding lipschitzian norm is independent of the viscosity. This allows us to prove some results related to the inviscid limit for the geometric structures of the vortex patch.
Propagation of chaos for the 2D viscous vortex model
We consider a stochastic system of particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly...
Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation.
Structural evolution of the Taylor vortices
Structural Evolution of the Taylor Vortices
We classify in this article the structure and its transitions/evolution of the Taylor vortices with perturbations in one of the following categories: a) the Hamiltonian vector fields, b) the divergence-free vector fields, and c). the solutions of the Navier-Stokes equations on the two-dimensional torus. This is part of a project oriented toward to developing a geometric theory of incompressible fluid flows in the physical spaces.
Transitional vortices in wide-gap spherical annulus flow.
Un résultat de décroissance des poches de tourbillon axisymétriques
Vorticity dynamics and numerical resolution of Navier-Stokes equations
We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical data...
Vorticity dynamics and numerical Resolution of Navier-Stokes Equations
We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical data...