# Vortex filament solutions of the Navier-Stokes equations

@article{Bedrossian2018VortexFS, title={Vortex filament solutions of the Navier-Stokes equations}, author={Jacob Bedrossian and Pierre Germain and Benjamin Harrop-Griffiths}, journal={arXiv: Analysis of PDEs}, year={2018} }

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…

## 3 Citations

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