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

2020 ◽  
Vol 73 (3) ◽  
pp. 217-230
Author(s):  
Siran Li
Keyword(s):  
Sobolev Spaces ◽  
Weak Solutions ◽  
Classical Model ◽  
Viscous Flows ◽  
Vortex Filament ◽  
Vorticity Equation ◽  
Geometrical Approach ◽  
Filament Dynamics ◽  
Incompressible Viscous Flows ◽  
Regularity Of Weak Solutions

Summary We 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.

15.—Differentiability on the Boundary of the Solutions of Linear Elliptic Boundary Value Problems

1975 ◽  
Vol 73 ◽  
pp. 235-249 ◽  
Author(s):  
Renate Schappel
Keyword(s):  
Functional Analysis ◽  
Boundary Value Problems ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Regularity Of Weak Solutions ◽  
Linear Elliptic Boundary

SynopsisThe present paper is concerned with the problem of regularity of weak solutions of boundary value problems. We shall present a new method to prove differentiability on the boundary. This method was developed in our thesis [12] within the theory of abstract Sobolev spaces, introduced by Stummel [14]. Here, we shall describe it by applying it to elliptic boundary value problems. It will be seen that the advantage of this method consists in the fact that it is based on functional analysis only and therefore may be used for other types of differential equations as well.

A local adaptive remeshing procedure for unsteady incompressible viscous flows

2020 ◽  
Author(s):  
Etienne Muller ◽  
Yohann Vautrin ◽  
Dominique Pelletier ◽  
Andre Garon
Keyword(s):  
Viscous Flows ◽  
Adaptive Remeshing ◽  
Incompressible Viscous Flows

Explicit and semi-implicit CBS procedures for incompressible viscous flows

2006 ◽  
Vol 66 (10) ◽  
pp. 1618-1640 ◽  
Author(s):  
N. Massarotti ◽  
F. Arpino ◽  
R. W. Lewis ◽  
P. Nithiarasu
Keyword(s):  
Viscous Flows ◽  
Incompressible Viscous Flows
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