Etude de formes d'equations universelles de type couche limite
Étude qualitatif des solutions des équations de Navier-Stokes en dimension 3
Euler and Navier-Stokes equations.
Eulerian formulation and level set models for incompressible fluid-structure interaction
This paper is devoted to Eulerian models for incompressible fluid-structure systems. These models are primarily derived for computational purposes as they allow to simulate in a rather straightforward way complex 3D systems. We first analyze the level set model of immersed membranes proposed in [Cottet and Maitre, Math. Models Methods Appl. Sci.16 (2006) 415–438]. We in particular show that this model can be interpreted as a generalization of so-called Korteweg fluids. We then extend this model...
Evaporation of Sessile Water Droplets in Presence of Contact Angle Hysteresis
In this paper we present a theory describing the diffusion limited evaporation of sessile water droplets in presence of contact angle hysteresis. Theory describes two stages of evaporation process: (I) evaporation with a constant radius of the droplet base; and (II) evaporation with constant contact angle. During stage (I) the contact angle decreases from static advancing contact angle to static receding contact angle, during stage (II) the contact...
Evaporation-driven Contact Angles in a Pure-vapor Atmosphere : the Effect of Vapor Pressure Non-uniformity
A small vicinity of a contact line, with well-defined (micro)scales (henceforth the “microstructure”), is studied theoretically for a system of a perfectly wetting liquid, its pure vapor and a superheated flat substrate. At one end, the microstructure terminates in a non-evaporating microfilm owing to the disjoining-pressure-induced Kelvin effect. At the other end, for motionless contact lines, it terminates in a constant film slope (apparent contact...
Exact boundary controllability of Galerkin's approximations of Navier-Stokes equations
Exact controllability in fluid – solid structure: The Helmholtz model
A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability...
Exact controllability in fluid–solid structure : the Helmholtz model
A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability results....
Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions.
Existence and uniqueness for optimal control of oxygen absorption in aquatic system.
Existence and uniqueness results for non-Newtonian fluids of the Oldroyd type in unbounded domains
In the paper [13], we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in [13] to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover, existence...
Existence et approximation de points selles pour certains problèmes non linéaires
Existence et comportement asymptotique en temps des solutions de Navier-Stokes Coriolis dans une bande tridimensionnelle
Existence for a stationary model of binary alloy solidification
Existence for an unsteady fluid-structure interaction problem
Existence for an Unsteady Fluid-Structure Interaction Problem
We study the well-posedness of an unsteady fluid-structure interaction problem. We consider a viscous incompressible flow, which is modelled by the Navier-Stokes equations. The structure is a collection of rigid moving bodies. The fluid domain depends on time and is defined by the position of the structure, itself resulting from a stress distribution coming from the fluid. The problem is then nonlinear and the equations we deal with are coupled. We prove its local solvability in time through two...
Existence globale pour un fluide inhomogène
Dans cet article on s’intéresse à l’existence et l’unicité globale de solutions pour le système de Navier-Stokes à densité variable, lorsque la donnée initiale de la vitesse est dans l’espace de Besov homogène de régularité critique . Notons que ce résultat fait suite aux résultats de H. Abidi qui a généralisé le travail de R. Danchin. Toutefois, dans les travaux antérieurs, l’existence de la solution est obtenue pour et l’unicité est démontrée sous l’hypothèse plus restrictive Notre résultat...
Existence of global solutions to the 2-D subcritical dissipative quasi-geostrophic equation and persistency of the initial regularity.
Existence of semi-periodic solutions of steady Navier-Stokes equations in a half space with an exponential decay at infinity