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

Jalal Shatah, Chongchun Zeng

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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.

Original languageEnglish (US)
Pages (from-to)698-744
Number of pages47
JournalCommunications on Pure and Applied Mathematics
Volume61
Issue number5
DOIs
Publication statusPublished - May 2008

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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