Regularity of Desingularized Models for Vortex Filaments in Incompressible Viscous Flows: A Geometrical Approach-Reference-Cited by-同舟云学术

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

Published:2020-05-20 Issue:3 Volume:73 Page:217-230
ISSN:0033-5614
Container-title:The Quarterly Journal of Mechanics and Applied Mathematics
language:en
Short-container-title:

Author:

Li Siran¹

Affiliation:

1. Department of Mathematics, Rice University, MS 136 P.O. Box 1892, Houston, Texas, 77251, USA

Abstract

SummaryWe establish the regularity of weak solutions for the vorticity equation associated to a family of desingularized models for vortex filament dynamics in 3D incompressible viscous flows. These generalize 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.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Link

http://academic.oup.com/qjmam/article-pdf/73/3/217/33667493/hbaa008.pdf

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