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Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations
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eBook
Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations
2018
Overview
This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in
fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves,
we can consider solutions such that the curvature of the initial free surface does not belong to
The
proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and
Hölder estimates. We first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then we use the dispersive
properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.
Publisher
American Mathematical Society
Subject
ISBN
9781470432034, 147043203X
