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SUMMARY:Vortex filaments for Euler equations - Monica Musso (University of
  Bath)
DTSTART:20220216T133000Z
DTEND:20220216T143000Z
UID:TALK167360@talks.cam.ac.uk
DESCRIPTION:We consider the Euler equations for incompressible fluids in 3
 -dimension. A classical question that goes back to Helmholtz is to describ
 e the evolution of vorticities with a high concentration around a cruve. T
 he 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 vortic
 ity 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. In this talk I will discuss the construction of helical filaments\,
  associated to a translating-rotating helix\, and of two vortex rings inte
 racting between each other\, the so-called leapfrogging. The results are i
 n collaboration with J. Davila (U. of Bath)\, M. del Pino (U. of Bath) and
  J. Wei (U. of British Columbia).
LOCATION:Seminar Room 1\, Newton Institute
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