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BCAMSevero Ochoa Award

basque center for applied mathematics

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Vega, Luis

The pictures of these section are related to the work I started with F. de la Hoz on 2013 about the Vortex Filament
Equation (also known under the names of Localized Induction Approximation and the Binormal Flow) for a
regular polygon. In this work we performed some numerical experiments establishing a connection with the so-called
Riemann's non differentiable function. After several works with V. Banica we have rigorously proved in
arXiv:2007.07184 that these experiments are correct.

Our results also suggest that if the initial datum is an equilateral triangle for later times the triangle should switch
the axis up and down each half of a period. Also for intermediate times skew polygons with a number of sides that
are multiple of three should be created like for example a skew polygon with six sides.

Below you will find some "domestic" experiments using a smoke cannon done with a card box. And finally some
experiments done in the James Franck Institute of the U. of Chicago (USA) and some numerical simulations done
by F. De La Hoz and S. Kumar.

Some Vortices

Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del País Vasco (UPV/EHU) Ayuntamiento de Bilbao - Bilboko Udala