Vortex Filament Solutions of the Navier-Stokes Equations

Jacob Bedrossian, Pierre Germain, Benjamin Harrop-Griffiths

Research output: Contribution to journalArticlepeer-review


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 that are locally approximately self-similar.

Original languageEnglish (US)
Pages (from-to)685-787
Number of pages103
JournalCommunications on Pure and Applied Mathematics
Issue number4
StatePublished - Apr 2023

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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