Well-posedness of 3D vortex sheets with surface tension

David M. Ambrose, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review

Abstract

We prove well-posedness for the initial value problem for a vortex sheet in 3D fluids, in the presence of surface tension. We first reformulate the problem by making a favorable choice of variables and parameterizations. We then perform energy estimates for the evolution equations. It is important to note that the Kelvin-Helmholtz instability is present for the vortex sheet in the absence of surface tension. Accordingly, we must construct the energy functional carefully with an eye toward the regularization of this instability. Well-posedness follows from the estimates.

Original languageEnglish (US)
Pages (from-to)391-430
Number of pages40
JournalCommunications in Mathematical Sciences
Volume5
Issue number2
DOIs
StatePublished - 2007

Keywords

  • Kelvin-Helmholtz instability
  • Surface tension
  • Vortex sheet
  • Well-posedness

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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