Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type
Kink solutions of the binormal flow
I shall present some recent work in collaboration with S. Gutierrez on the characterization of all selfsimilar solutions of the binormal flow : which preserve the length parametrization. Above is a curve in , the arclength parameter, and denote the temporal variable. This flow appeared for the first time in the work of Da Rios (1906) as a crude approximation to the evolution of a vortex filament under Euler equation, and it is intimately related to the focusing cubic nonlinear Schrödinger...
Le problème des poches de tourbillon en dimension trois d'espace
Les équations de Kelvin-Helmotz. Un problème bien posé uniquement dans le cadre analytique
Localized induction equation for stretched vortex filament.
Mechanical analogy for the wave-particle: Helix on a vortex filament.
Motion of two point vortices in a steady, linear, and elliptical flow.
Nested axi-symmetric vortex rings
Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation.
Nonlinear instability in an ideal fluid
Numerical evidence of nonuniqueness in the evolution of vortex sheets
We consider a special configuration of vorticity that consists of a pair of externally tangent circular vortex sheets, each having a circularly symmetric core of bounded vorticity concentric to the sheet, and each core precisely balancing the vorticity mass of the sheet. This configuration is a stationary weak solution of the 2D incompressible Euler equations. We propose to perform numerical experiments to verify that certain approximations of this flow configuration converge to a non-stationary...
On L1-Vorticity for 2-D incompressible flow.
On the chaotic behavior and the non-integrability of the four vortices problem
On the Euler equations with a singular external velocity field
On the existence and the regularity of an initial boundary problem of vorticity equation
On the localization of the vortices
Studiamo l'evoluzione temporale di un fluido bidimensionale incomprimibile non viscoso quando la vorticità iniziale è concentrata in regioni di diametro e mostriamo che la vorticità evoluta temporalmente è anche lei concentrata in piccole regioni di diametro , per qualunque . Noi chiamiamo questa proprietà "localizzazione". Come conseguenza abbiamo una connessione rigorosa tra il modello dei vortici puntiformi e l'Equazione di Eulero.
On the motion of a curve by its binormal curvature
We propose a weak formulation for the binormal curvature flow of curves in . This formulation is sufficiently broad to consider integral currents as initial data, and sufficiently strong for the weak-strong uniqueness property to hold, as long as self-intersections do not occur. We also prove a global existence theorem in that framework.
On three-dimensional vortex patches
On two-dimensional and three dimensional axially-symmetric rotational flows of an ideal incompressible fluid
Persistance de structures géométriques dans les fluides incompressibles bidimensionnels