Geodesic
Transport of interfaces with surface tension by 2D viscous flows
David M. Ambrose1 ; Milton C. Lopes Filho2 ; Helena J. Nussenzveig Lopes2 ; Walter A. Strauss3 orcid
1Drexel University, Philadelphia, USA
2IMECC - UNICAMP, Campinas, Brazil
3Brown University, Providence, USA
Interfaces and free boundaries, Tome 12 (2010) no. 1, pp. 23-44

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DOI

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 Plotnikov in [16] and Abels in [1]. 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.
DOI : 10.4171/ifb/225
Classification : 35-XX, 65-XX, 76-XX, 92-XX

David M. Ambrose  1   ; Milton C. Lopes Filho  2   ; Helena J. Nussenzveig Lopes  2   ; Walter A. Strauss  3

1 Drexel University, Philadelphia, USA
2 IMECC - UNICAMP, Campinas, Brazil
3 Brown University, Providence, USA 
David M. Ambrose; Milton C. Lopes Filho; Helena J. Nussenzveig Lopes; Walter A. Strauss. Transport of interfaces with surface tension by 2D viscous flows. Interfaces and free boundaries, Tome 12 (2010) no. 1, pp. 23-44. doi: 10.4171/ifb/225
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     title = {Transport of interfaces with surface tension by {2D} viscous flows},
     journal = {Interfaces and free boundaries},
     pages = {23--44},
     year = {2010},
     volume = {12},
     number = {1},
     doi = {10.4171/ifb/225},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/225/}
}
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