Well-posedness of the free-surface incompressible Euler equations with or without surface tension |
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| Authors: | Daniel Coutand Steve Shkoller |
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| Institution: | Department of Mathematics, University of California at Davis, Davis, California 95616 ; Department of Mathematics, University of California at Davis, Davis, California 95616 |
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| Abstract: | 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. |
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| Keywords: | Euler equations free boundary problems surface tension |
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