Fifth Itinerant Workshop on PDEs

course: The evolution of vortex filaments with corners (Part I and II)

speaker: Luis Vega (BCAM/UPV-EHU, Universidad Pais Vasco)

abstract: I shall present some work done in collaboration with V. Banica about the evolution of an infinite filament with one corner and some more recent results done with F. de la Hoz on the evolution of a regular polygon. The geometric flow we consider is the so called Localized Induction Approximation. According to it the filament moves in the direction of the binormal with a speed that is proportional to the curvature. In the work with Banica we prove that the process of creationannihilation of a one corner is stable. With De la Hoz we give theoretical and numerical arguments to show that the dynamics of a regular polygon involve fractals. We also make a connection about their dimension and the so called Frisch-Parisi conjecture for fully developed turbulence

timetable:
Fri 24 Jan, 9:00 - 11:00, Aula Dini
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