Étude numérique des pôles de résonance associés à la diffraction d'ondes acoustiques et élastiques par un obstacle en dimension 2
Étude qualitatif des solutions des équations de Navier-Stokes en dimension 3
Étude sur le timbre des sons, produits par des chocs discontinus et en particulier par la sirène
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...
Evolution by the vortex filament equation of curves with a corner
In this proceedings article we shall survey a series of results on the stability of self-similar solutions of the vortex filament equation. This equation is a geometric flow for curves in and it is used as a model for the evolution of a vortex filament in fluid mechanics. The main theorem give, under suitable assumptions, the existence and description of solutions generated by curves with a corner, for positive and negative times. Its companion theorem describes the evolution of perturbations...
Évolution de tourbillon à support compact
On considère l’équation d’Euler incompressible dans le plan. Dans le cas où le tourbillon est positif et à support compact on montre que le support du tourbillon croît au plus comme , améliorant la borne obtenue par C. Marchioro. Dans le cas où le tourbillon change de signe, on donne un exemple de tourbillon initial tel que la croissance du diamètre du support du tourbillon est exactement . Enfin, dans le cas du demi-plan et du tourbillon initial positif et à support compact, on montre que le...
Évolution d'une singularité de type cusp dans une poche de tourbillon
Évolution d'une singularité de type cusp dans une poche de tourbillon.
We investigate the evolution of singularities in the boundary of a vortex patch for two-dimensional incompressible Euler equations. We are particularly interested in cusp-like singularities which, according to numerical simulations, are stable. In this paper, we first prove that, unlike the case of a corner-like singularity, the cusp-like singularity generates a lipschitzian velocity. We then state a global result of persistence of conormal regularity with respect to vector fields vanishing at a...
Evolution of fluid-fluid interface in porous media as the model of gas-oil fields.
Evolution of shock waves in relativistic continuum mechanics
Exact boundary controllability of 3-D Euler equation
Exact boundary controllability of 3-D Euler equation
We prove the exact boundary controllability of the 3-D Euler equation of incompressible inviscid fluids on a regular connected bounded open set when the control operates on an open part of the boundary that meets any of the connected components of the boundary.
Exact boundary controllability of a nonlinear KdV equation with critical lengths
We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.
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....
Exact solution of the time fractional variant Boussinesq-Burgers equations
In the present article, we consider a nonlinear time fractional system of variant Boussinesq-Burgers equations. Using Lie group analysis, we derive the infinitesimal groups of transformations containing some arbitrary constants. Next, we obtain the system of optimal algebras for the symmetry group of transformations. Afterward, we consider one of the optimal algebras and construct similarity variables, which reduces the given system of fractional partial differential equations (FPDEs) to fractional...