Transport of interfaces with surface tension by 2D viscous flows
type: Item
instance of: scholarly article
title: Transport of interfaces with surface tension by 2D viscous flows
zbMATH Open document ID: 1189.35238
DOI: 10.4171/IFB/225
author: David M. Ambrose
author: Walter A. Strauss
author: Milton C. Lopes Filho
author: Helena J. Nussenzveig Lopes
published in: Interfaces and Free Boundaries
publication date: 2010-04-08T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/all_issues.php
review text: Summary: We consider the problem of finding a global weak solution for two-dimensional, incompressible viscous flow on a torus, containing a surface-tension bearing curve transported by the flow. This is the simplest case of a class of two-phase flows considered by \textit{P. I. Plotnikov} [Sib. Math. J. 34, No.~4, 704--716 (1993); translation from Sib. Mat. Zh. 34, No.~4, 127--141 (1993; Zbl 0814.76007)] and \textit{H. Abels} [Interfaces Free Bound. 9, No.~1, 31--65 (2007; Zbl 1124.35060)]. Our work complements Abels' analysis by examining this special case in detail. We construct a family of approximations and show that the limit of these approximations satisfies, globally in time, an incomplete set of equations in the weak sense. In addition, we examine criteria for closure of the limit system, we find conditions which imply nontrivial dependence of the limiting solution on the surface tension parameter, and we obtain a new system of evolution equations which models our flow-interface problem, in a form that may be useful for further analysis and for numerical simulations.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 76D45
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 76T99
zbMATH DE Number: 5690536
zbMATH Keywords: surface tension
zbMATH Keywords: Eulerian interface dynamics
zbMATH Keywords: flow-interface problem
zbMATH Keywords: torus
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5690536