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Vortex filament solutions for the Navier-Stokes equations

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

April 30, 2021 (09:00 AM PDT - 09:50 AM PDT)
Speaker(s): Pierre Germain (New York University, Courant Institute)
Location: MSRI: Online/Virtual
Tags/Keywords
  • vortex filaments

  • Navier-Stokes

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Abstract

I will present a construction of solutions of the Navier-Stokes equations for data whose vorticity are concentrated on 1D curves (as measures). This corresponds to large locally self-similar data, for which the usual perturbative approach to local well-posedness does not apply, and for which a number of interesting questions arise. These data are also of fundamental importance from a physical perspective, since vortex filaments are expected to play a crucial role in 3D flows. This is joint work with J. Bedrossian and B. Harrop-Griffiths.

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