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

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arxiv math/0608428 v2 pith:CWCZR3VS submitted 2006-08-16 math.AP math.DG

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

Jalal Shatah , Chongchun Zeng This is my paper
classification math.AP math.DG
keywords surfacetensioneulerboundaryconditionequationestimatesfree
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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 zero, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler flow with zero surface tension.

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