### 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) |
---|---|

Pages (from-to) | 347-373 |

Number of pages | 27 |

Journal | Journal of Hyperbolic Differential Equations |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2011 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Journal of Hyperbolic Differential Equations*, vol. 8, no. 2, pp. 347-373. https://doi.org/10.1142/S021989161100241X

}

TY - JOUR

T1 - On the limit as the surface tension and density ratio tend to zero for the two-phase euler equations

AU - Pusateri, Fabio

AU - Masmoudi, N.

PY - 2011/6

Y1 - 2011/6

N2 - 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.

AB - 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.

KW - Euler equations

KW - surface tension

KW - vortex-sheet problem

UR - http://www.scopus.com/inward/record.url?scp=79959970992&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959970992&partnerID=8YFLogxK

U2 - 10.1142/S021989161100241X

DO - 10.1142/S021989161100241X

M3 - Article

AN - SCOPUS:79959970992

VL - 8

SP - 347

EP - 373

JO - Journal of Hyperbolic Differential Equations

JF - Journal of Hyperbolic Differential Equations

SN - 0219-8916

IS - 2

ER -