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Séminaire du LJLL - 21 05 2021 14h00 : J. Bedrossian
21 mai 2021 — 14h00
Exposé à distance retransmis par Zoom
Jacob Bedrossian (Université du Maryland, College Park)
Vortex filament solutions of the 3d Navier-Stokes equations
Résumé
We consider solutions of the Navier-Stokes equations in 3d with vortex filament initial data of arbitrary circulation, that is, initial vorticity given by a divergence-free vector-valued measure of arbitrary mass supported on a smooth curve. First, we prove global well-posedness for perturbations of the Oseen vortex column in scaling-critical spaces. Second, we prove local well-posedness (in a sense to be made precise) when the filament is a smooth, closed, non-self-intersecting curve. Besides their physical interest, these results are the first to give well-posedness results in a neighborhood of large self-similar solutions of the 3d Navier-Stokes equations, as well as solutions which are locally approximately self-similar.
This is joint work with Pierre Germain and Benjamin Harrop-Griffiths.