Strong solutions of the steady nonlinear Navier-Stokes system in domains with exits to infinity
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.
Study of a three component Cahn-Hilliard flow model
In this paper, we propose a new diffuse interface model for the study of three immiscible component incompressible viscous flows. The model is based on the Cahn-Hilliard free energy approach. The originality of our study lies in particular in the choice of the bulk free energy. We show that one must take care of this choice in order for the model to give physically relevant results. More precisely, we give conditions for the model to be well-posed and to satisfy algebraically and dynamically consistency...
Su un problema esterno relativo alle equazioni di Navier-Stokes
Sull'evoluzione del profilo di velocità in moto laminare a bassi numeri di Reynolds
The development of velocity distribution in plane laminar flow is examined, neglecting inertial terms in respect to viscous ones. A solution is given, which satisfies all boundary conditions.
Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method
This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of Li et al. (2012), which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis.
Sur la propagation de quasi-singularités
Sur le temps de vie de la turbulence bidimensionnelle
On sait que toutes les solutions de l’équation de Navier-Stokes dans dont le tourbillon est intégrable convergent lorsque vers un écoulement autosimilaire appelé tourbillon d’Oseen. Dans cet article, nous donnons une estimation du temps nécessaire à la solution pour atteindre un voisinage du tourbillon d’Oseen à partir d’une donnée initiale arbitraire, mais bien localisée en espace. Nous obtenons ainsi une borne supérieure sur le temps de vie de la turbulence bidimensionnelle libre, en fonction...
Sur l’équation de Prandtl
L’objet de cette note est le problème de Cauchy pour l’équation de Prandtl, dans des espaces de régularité Sobolev. Nous discutons de façon synthétique des résultats récents [4], établissant le caractère fortement linéairement mal posé de ce problème.
Sur l'évolution des mesures déterminées par les équations de Navier-Stokes et la résolution du problème de Cauchy pour l'équation statistique de E. Hopf
Sur l’unicité dans le système de Navier-Stokes tridimensionnel
The 3D Happel model for complete isotropic Stokes flow.
The 3D navier-stokes equations seen as a perturbation of the 2D navier-stokes equations
The Asymptotics of the Heat Equation for a Boundary Value Problem.
The basic boundary value problems of static elasticity theory and their Cosserat spectrum.
The Blasius function in the complex plane.
The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure
We assume that is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of .
The Cauchy problem and decay rates for strong solutions of a Boussinesq system.
The Cauchy problem for the homogeneous time-dependent Oseen system in : spatial decay of the velocity
We consider the homogeneous time-dependent Oseen system in the whole space . The initial data is assumed to behave as , and its gradient as , when tends to infinity, where is a fixed positive number. Then we show that the velocity decays according to the equation , and its spatial gradient decreases with the rate , for tending to infinity, uniformly with respect to the time variable . Since these decay rates are optimal even in the stationary case, they should also be the best possible...