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16 Ottobre, 2024 15:00
Sezione di Analisi per il Dipartimento di Eccellenza (interazioni fluido-strutture)

Global well-posedness of 3D Navier-Stokes with helical vortex filament data

Antonio Hidalgo-Torné, Max Planck Institute for Mathematics in the Sciences, Leipzig
Aula Seminari - III Piano
Abstract

We address the global-in-time existence, uniqueness, and regularity of solutions to the Cauchy problem for the three-dimensional Navier-Stokes equation with the initial vorticity concentrated on a helix. More specifically, we establish a local-in-time well-posedness result for vortex filaments that are periodic in one spatial direction, following the approach of Bedrossian, Germain and Harrop-Griffiths for closed filaments. Then, we use local energy weak solutions and helical estimates to extend the solution uniquely and globally in time in the helical case.