On the limit as the density ratio tends to zero for two perfect incompressible fluids separated by a surface of discontinuity

C. H A Cheng, Daniel Coutand, Steve Shkoller

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We study the asymptotic limit as the density ratio ?-/?+ ? 0, where ?+ and ?- are the densities of two perfect incompressible 2-D/3-D fluids, separated by a surface of discontinuity along which the pressure jump is proportional to the mean curvature of the moving surface. Mathematically, the fluid motion is governed by the two-phase incompressible Euler equations with vortex sheet data. By rescaling, we assume the density ?+ of the inner fluid is fixed, while the density ?- of the outer fluid is set to e. We prove that solutions of the free-boundary Euler equations in vacuum are obtained in the limit as e ? 0. © Taylor & Francis Group, LLC.

Original languageEnglish
Pages (from-to)817-845
Number of pages29
JournalCommunications in Partial Differential Equations
Volume35
Issue number5
DOIs
Publication statusPublished - May 2010

Keywords

  • Euler equations
  • Surface tension
  • Two-phase flow
  • Vortex sheets
  • Water waves
  • Zero density limit

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