A confinement result for axisymmetric fluids
A global branch of steady vortex rings.
A new approach for the analysis of Vortex Methods in two and three dimensions
A note on asymptotic helix and quantum mechanical structure.
A numerical study of some questions in vortex rings theory
A Potential Method for the Biharmonic Equation.
Adaptive panel representation for 3D vortex ring motion and instability.
Asymptotic behaviour in planar vortex theory
The asymptotic behaviour of solutions of a class of free-boundary problems arising in vortex theory is discussed.
Asymptotic stability of a stationary flowing regime of an ideal incompressible fluid.
Blow-up in a modified Constantin-Lax-Majda model for the vorticity equation.
Conforming equilibrium finite element methods for some elliptic plane problems
Entrée-sortie dans un tourbillon
On étudie un champ de vecteurs lent-rapide de nommé tourbillon pour lequel on démontre l’existence d’une fonction entrée-sortie.
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...
Existence de nappes de tourbillon pour l'équation d'Euler sur le plan
Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data.
Existence of threedimensional, steady, inviscid, incompressible flows with nonvanishing vorticity.
Helmholtz's vorticity transport equation with partial discretization in bounded 3-dimensional domains.