Regularity of Desingularised Models for Vortex Filaments in Incompressible Viscous Flows: A Geometrical Approach

Abstract

We establish the regularity of weak solutions for the vorticity equation associated to a family of desingularised models for vortex filament dynamics in 3D incompressible viscous flows. These include and generalise the classical model "of an allowance for the thickness of the vortices" due to Louis Rosenhead in 1930. Our approach is based on an interplay between the geometry of vorticity and analytic inequalities in Sobolev spaces.

arXiv comment11 pages. Quarterly Journal of Mechanics and Applied Mathematics (2020)