On the limit as the surface tension and density ratio tend to zero for the two-phase euler equations

Fabio Pusateri, N. Masmoudi

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

We consider the free boundary motion of two perfect incompressible fluids with different densities ρ+ and ρ-, separated by a surface of discontinuity along which the pressure experiences a jump proportional to the mean curvature by a factor ε2. Assuming the RayleighTaylor sign condition, and ρ- ≤ ε3/2, we prove energy estimates uniform in ρ- and ε. As a consequence, we obtain convergence of solutions of the interface problem to solutions of the free boundary Euler equations in vacuum without surface tension as ε, ρ- → 0.

Original languageEnglish (US)
Pages (from-to)347-373
Number of pages27
JournalJournal of Hyperbolic Differential Equations
Volume8
Issue number2
DOIs
StatePublished - Jun 1 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

Keywords

  • Euler equations
  • surface tension
  • vortex-sheet problem

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