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

Jalal Shatah; Chongchun Zeng

doi:10.1002/cpa.20213

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

Jalal Shatah, Chongchun Zeng

Mathematics

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	698-744
Number of pages	47
Journal	Communications on Pure and Applied Mathematics
Volume	61
Issue number	5
DOIs	https://doi.org/10.1002/cpa.20213
State	Published - May 2008

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/cpa.20213

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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.",

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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.

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

Abstract

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