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CATEGORIES:Analysis seminar
SUMMARY:Leapfrogging for Euler equations - Monica Musso\,
University of Bath
DTSTART:20221024T140000Z
DTEND:20221024T150000Z
UID:TALK4970AT
URL:/talk/index/4970
DESCRIPTION:We consider the Euler equations for incompressible
fluids in 3-dimension. A classical question that
goes back to Helmholtz is to describe the evolutio
n of vorticities with a high concentration around
a curve. The work of Da Rios in 1906 states that s
uch a curve must evolve by the so-called "binormal
curvature flow". Existence of true solutions whos
e vorticity is concentrated near a given curve tha
t evolves by this law is a long-standing open ques
tion that has only been answered for the special c
ase of a circle travelling with constant speed alo
ng its axis\, the thin vortex-rings. In this talk
I will discuss the construction of helical filamen
ts\, associated to a translating-rotating helix\,
and of two vortex rings interacting between each o
ther\, 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 C
olumbia).
LOCATION:WATN-LT C (G24)
CONTACT:Yuzhao Wang
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