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

• Autores: Daniel Coutand, Steve Shkoller
• Localización: Journal of the American Mathematical Society, ISSN 0894-0347, Vol. 20, Nº 3, 2007, págs. 829-930
• Idioma: inglés
• DOI: 10.1090/s0894-0347-07-00556-5
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• Resumen

  • 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