• Corpus ID: 119560945

Vortex filament solutions of the Navier-Stokes equations

  title={Vortex filament solutions of the Navier-Stokes equations},
  author={Jacob Bedrossian and Pierre Germain and Benjamin Harrop-Griffiths},
  journal={arXiv: Analysis of PDEs},
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… 

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