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Vortex filament solutions of the Navier-Stokes equations
PDE and Applied Math Seminar| Speaker: | Benjamin Harrop-Griffiths, UCLA |
| Location: | Zoom |
| Start time: | Thu, Apr 28 2022, 4:10PM |
From Helmholtz to vaping hipsters, understanding the dynamics of vortex filaments remains one of the most interesting and important problems in fluid dynamics. Vortex filaments with small circulation can be treated as mild solutions of the 3d Navier-Stokes equations in scaling-critical spaces. However, these results do not apply to filaments with large circulations. In this talk, we first consider well-posedness in a neighborhood of the Oseen vortex, a large self-similar solution of the 3d Navier-Stokes equations. We then discuss local well-posedness for arbitrary smooth vortex filaments. This is joint work with Jacob Bedrossian and Pierre Germain.