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Vortex filament solutions of the 3D Navier-Stokes equations

[Moved Online] Recent Developments in Fluid Dynamics April 12, 2021 - April 30, 2021

April 26, 2021 (09:00 AM PDT - 09:50 AM PDT)
Speaker(s): Jacob Bedrossian (University of Maryland)
Location: MSRI: Online/Virtual
Tags/Keywords
  • 3d Navier-Stokes

  • Self-similar solutions

  • critical data

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Abstract

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 in a neighborhood of large self-similar solutions of 3d Navier-Stokes, as well as solutions which are locally approximately self-similar. This is joint work with Pierre Germain and Benjamin Harrop-Griffiths.

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