### 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 language | English (US) |
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Pages (from-to) | 347-373 |

Number of pages | 27 |

Journal | Journal of Hyperbolic Differential Equations |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2011 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematics(all)

### Keywords

- Euler equations
- surface tension
- vortex-sheet problem

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## Cite this

Pusateri, F., & Masmoudi, N. (2011). On the limit as the surface tension and density ratio tend to zero for the two-phase euler equations.

*Journal of Hyperbolic Differential Equations*,*8*(2), 347-373. https://doi.org/10.1142/S021989161100241X