### 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 language | English |
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Pages (from-to) | 817-845 |

Number of pages | 29 |

Journal | Communications in Partial Differential Equations |

Volume | 35 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2010 |

### Keywords

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

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## Cite this

*Communications in Partial Differential Equations*,

*35*(5), 817-845. https://doi.org/10.1080/03605300903503115