Strichartz estimates and the Cauchy problem for the gravity water waves equations. Memoirs of the American Mathematical Society; Bd. volume 256, number 1229 (fifth of 6 numbers).

Alazard, T.; Burq, N.; Zuily, C.

ISBN 10: 147043203X / ISBN 13: 9781470432034

Published by Providence, American Mathematical Society, 2018

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-03358 9781470432034 Sprache: Englisch Gewicht in Gramm: 150.

Seller Inventory # 2489265

Bibliographic Details

• Title: Strichartz estimates and the Cauchy problem for the gravity water waves equations. Memoirs of the American Mathematical Society; Bd. volume 256, number 1229 (fifth of 6 numbers).
• Publisher: Providence, American Mathematical Society
• Publication Date: 2018
• Language: English
• ISBN 10: 147043203X
• ISBN 13: 9781470432034
• Binding: Softcover
• Condition: Gut
• Weight: 150 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

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, the authors consider solutions such that the curvature of the initial free surface does not belong to $L2$. 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.