### Abstract

In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to 0, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler flow with zero surface tension.

Original language | English (US) |
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Pages (from-to) | 698-744 |

Number of pages | 47 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 61 |

Issue number | 5 |

DOIs | |

State | Published - May 2008 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*61*(5), 698-744. https://doi.org/10.1002/cpa.20213

**Geometry and a priori estimates for free boundary problems of the Euler equation.** / Shatah, Jalal; Zeng, Chongchun.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 61, no. 5, pp. 698-744. https://doi.org/10.1002/cpa.20213

}

TY - JOUR

T1 - Geometry and a priori estimates for free boundary problems of the Euler equation

AU - Shatah, Jalal

AU - Zeng, Chongchun

PY - 2008/5

Y1 - 2008/5

N2 - In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to 0, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler flow with zero surface tension.

AB - In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to 0, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler flow with zero surface tension.

UR - http://www.scopus.com/inward/record.url?scp=52349104032&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52349104032&partnerID=8YFLogxK

U2 - 10.1002/cpa.20213

DO - 10.1002/cpa.20213

M3 - Article

AN - SCOPUS:52349104032

VL - 61

SP - 698

EP - 744

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 5

ER -