Well-posedness of the free-surface incompressible Euler equations with or without surface tension

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We provide a new method for treating free boundary problems in perfect fluids, and prove local-in-time well-posedness in Sobolev spaces for the free-surface incompressible 3D Euler equations with or without surface tension for arbitrary initial data, and without any irrotationality assumption on the fluid. This is a free boundary problem for the motion of an incompressible perfect liquid in vacuum, wherein the motion of the fluid interacts with the motion of the free-surface at highest-order.
To appear in J. Amer. Math. Soc., 96 pages

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Analysis of PDEs, Mathematical Physics, 35Q35, 35R35, 35Q05, 76B03

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http://salesiana.dossiersoluciones.com/handle/123456789/104857

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511236
 http://arxiv.org/abs/math/0511236

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arXiv