# 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

Non-uniqueness of Leray solutions of the forced Navier-Stokes equations

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- 2021

In the seminal work [39], Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. We exhibit two distinct Leray solutions with zero initial…

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We prove an $\epsilon$-regularity criterion for the 3D Navier-Stokes equations in terms of initial data. It shows that if a scaled local $L^2$ norm of initial data is sufficiently small around the…

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- Physics, Mathematics
- 2020

Abstract In this paper, we consider the uniqueness of solutions to the 3d Navier-Stokes equations with initial vorticity given by where is the one dimensional Hausdorff measure of an infinite,…

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