Regularity of Desingularised Models for Vortex Filaments in Incompressible Viscous Flows: A Geometrical Approach
Analysis of PDEs
2020-09-01 v2
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.
Keywords
Cite
@article{arxiv.1801.04511,
title = {Regularity of Desingularised Models for Vortex Filaments in Incompressible Viscous Flows: A Geometrical Approach},
author = {Siran Li},
journal= {arXiv preprint arXiv:1801.04511},
year = {2020}
}
Comments
11 pages. Quarterly Journal of Mechanics and Applied Mathematics (2020)