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

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 ε 2. Assuming the RayleighTaylor sign condition, and ρ - ≤ ε 3/2, 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 2011

Fingerprint

Free Boundary
Euler Equations
Surface Tension
Tend
Interface Problems
Convergence of Solutions
Perfect Fluid
Energy Estimates
Zero
Mean Curvature
Incompressible Fluid
Discontinuity
Vacuum
Jump
Directly proportional
Motion
Experience

Keywords

  • Euler equations
  • surface tension
  • vortex-sheet problem

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

On the limit as the surface tension and density ratio tend to zero for the two-phase euler equations. / Pusateri, Fabio; Masmoudi, N.

In: Journal of Hyperbolic Differential Equations, Vol. 8, No. 2, 06.2011, p. 347-373.

Research output: Contribution to journalArticle

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