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September  2010, 3(3): 429-449. doi: 10.3934/dcdss.2010.3.429

A simple proof of well-posedness for the free-surface incompressible Euler equations

Daniel Coutand 1, and  Steve Shkoller 2,

1. 

Maxwell Institute for Mathematical Sciences and department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom
2. 

Department of Mathematics, University of California, Davis, CA 95616

Received  November 2009 Revised  January 2010 Published  May 2010

The purpose of this this paper is to present a new simple proof for the construction of unique solutions to the moving free-boundary incompressible 3-D Euler equations in vacuum. Our method relies on the Lagrangian representation of the fluid, and the anisotropic smoothing operation that we call horizontal convolution-by-layers. The method is general and can be applied to a number of other moving free-boundary problems.
Keywords: Euler, free boundary problems, vacuum., water-waves.
Mathematics Subject Classification: 35L65, 35L70, 35L80, 35Q35, 35R35, 76B0.
Citation: Daniel Coutand, Steve Shkoller. A simple proof of well-posedness for the free-surface incompressible Euler equations. Discrete & Continuous Dynamical Systems - S, 2010, 3 (3) : 429-449. doi: 10.3934/dcdss.2010.3.429
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