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OverviewThis 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, the authors consider solutions such that the curvature of the initial free surface does not belong to $L^2$. The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Holder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Holder norms and then use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Holder norms. Full Product DetailsAuthor: T. Alazard , N. Burq , C. ZuilyPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.185kg ISBN: 9781470432034ISBN 10: 147043203 Pages: 108 Publication Date: 30 January 2019 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationT. Alazard, Ecole Normale Superieure, Paris, France. N. Burq, Universite Paris-Sud, Orsay, France. C. Zuily, Universite Paris-Sud, Orsay, France. Tab Content 6Author Website:Countries AvailableAll regions |
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