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

Coutand, Daniel¹ ; Shkoller, Steve¹

¹ Department of Mathematics, University of California at Davis, Davis, California 95616

Journal of the American Mathematical Society, Tome 20 (2007) no. 3, pp. 829-930

Résumé

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.

Détail

DOI : 10.1090/S0894-0347-07-00556-5

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