A Note on the Asymptotic Behavior of 2d Gravity Water Waves
نویسندگان
چکیده
In this note we explain how to derive an asymptotic formula for solutions of the 2d gravity water waves system expressed in Eulerian coordinates, using some of the bounds obtained by the authors in [IPu13]. The main ingredients of the proof are: 1) the uniform estimates for the Fourier transform of the profile of solutions obtained in [IPu13], 2) a refined linear estimate for the propagator exp(it|∂x|), and 3) an argument similar to the one used by Hayashi and Naumkin in [HN98] in the context of NLS type equations.
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