Transport of interfaces with surface tension by 2D viscous flows

Autor(es)

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

Afiliação do(s) autor(es)

^[1] Drexel Univ, Dept Math, Philadelphia, PA 19104 - USA

^[2] Univ Estadual Campinas, UNICAMP, IMECC, Dept Matemat, BR-13083970 Campinas, SP - Brazil

^[3] Brown Univ, Dept Math, Providence, RI 02912 - USA

• Tipo de documento: Artigo Científico
• Fonte: INTERFACES AND FREE BOUNDARIES; v. 12, n. 1, p. 23-44, 2010.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 07/51490-7 - Aspectos matemáticos da dinâmica dos fluidos incompressíveis
• Beneficiário: Milton da Costa Lopes Filho
• Modalidade de apoio: Auxílio à Pesquisa - Temático