249 citations · 684 across the 32 of their papers we have counts for
4 papers · 1 filter
Strichartz estimates for gravity water waves
Thomas Alazard, Nicolas Burq, Claude Zuily
We prove Strichartz estimates for gravity water waves, in arbitrary dimension and in fluid domains with general bottoms. We consider rough solutions such that, initially, the first…
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…
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…
Cauchy theory for the gravity water waves system with non localized initial data
Thomas Alazard, Nicolas Burq, Claude Zuily
In this article, we develop the local Cauchy theory for the gravity water waves system, for rough initial data which do not decay at infinity. We work in the context of -based…