Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle. 1st ed. 2018

種類:

電子ブック

責任表示:

by Massimiliano Berti, Jean-Marc Delort

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Berti, Massimiliano.
• Delort, Jean-Marc.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes of the Unione Matematica Italiana ; 24

ISBN:

9783319994864 [3319994867]    

注記:

The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reduct

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