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math.AP2013
Sobolev estimates for two dimensional gravity water waves
Thomas Alazard, Jean-Marc Delort
Our goal in this paper is to apply a normal forms method to estimate the Sobolev norms of the solutions of the water waves equation. We construct a paradifferential change of unkno…
math.AP2013
Global solutions and asymptotic behavior for two dimensional gravity water waves
Thomas Alazard, Jean-Marc Delort
This paper is devoted to the proof of a global existence result for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asympto…