Vortex Filament Solutions of the Navier-Stokes Equations |
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| Authors: | Jacob Bedrossian Pierre Germain Benjamin Harrop-Griffiths |
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| Institution: | 1. University of Maryland, Department of Mathematics, 4176 Campus Drive, College Park, MD, 20742;2. Imperial College London, Huxley Building, South Kensigton Campus, London, SW7 2AZ United Kingdom;3. Georgetown University, Department of Mathematics and Statistics, St Mary's Hall, 37th and O Street, N.W, Washington, DC, 20057 USA |
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| Abstract: | 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. © 2023 Wiley Periodicals LLC. |
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