Analysis and PDE Seminar: Vortex filament solutions of the Navier-Stokes equations

Seminar | December 10 | 4:10-5 p.m. | 740 Evans Hall

 Benjamin Harrop-Griffiths, UCLA

 Department of Mathematics

From Helmholtz to vaping hipsters, the dynamics of vortex filaments, i.e. fluids with vorticity concentrated along a smooth curve, has been a topic of significant interest in fluid dynamics. The global well-posedness of vortex filaments with small circulation follows from the theory of mild solutions of the 3d Navier-Stokes equations at critical regularity. However, for filaments with large circulation these results no longer apply. In this talk we discuss a proof of well-posedness (in a suitable sense) for vortex filaments of arbitrary circulation. Besides their physical interest, these results are the first to give well-posedness in a neighborhood of large self-similar solutions of the 3d Navier-Stokes without additional symmetry assumptions. This is joint work with Jacob Bedrossian and Pierre Germain.

 tdepoyfe@math.berkeley.edu