Top-level heading

Leapfrogging for Euler equations

Categoria
Seminari di Analisi Matematica
Data e ora inizio evento
Data e ora fine evento
Aula
Sala di Consiglio
Sede

Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma

Speaker

Monica Musso (University of Bath)

We consider the Euler equations for incompressible fluids in 3-dimension. A classical question that goes back to Helmholtz is to describe the evolution of vorticities with a high concentration around a curve. The work of Da Rios in 1906 states that such a curve must evolve by the so-called "binormal curvature flow". Existence of true solutions whose vorticity is concentrated near a given curve that evolves by this law is a long-standing open question that has only been answered for the special case of a circle travelling with constant speed along its axis, the thin vortex-rings, and of a helical filament, associated to a translating-rotating helix. In this talk I will consider the case of two vortex rings interacting between each other, the so-called leapfrogging. The results are in collaboration with J. Davila (U. of Bath), M. del Pino (U. of Bath) and J. Wei (U. of British Columbia).