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

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

2006-08-16

arxiv.org/abs/math/0608428v2

Mathematics

Analysis of PDEs

33 pages, submitted, added references

Scientific paper

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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