• Accueil   >  
  • Reference   >  
  • Mathematics   >  
  • Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle
Téléchargez le livre : Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle

Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle



de

,

Éditeur :

Springer


Collection :

Lecture Notes of the Unione Matematica Italiana

Paru le : 2018-11-02



eBook Téléchargement , DRM LCP 🛈 DRM Adobe 🛈
Lecture en ligne (streaming)
47,46 €
Téléchargement immédiat
Dès validation de votre commande
Ajouter à ma liste d'envies
Image Louise Reader présentation

Louise Reader

Lisez ce titre sur l'application Louise Reader.

badge apple Application Louise Reader
badge Android Application Louise Reader
Description

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 reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.
Pages
269 pages
Collection
Lecture Notes of the Unione Matematica Italiana
Parution
2018-11-02
Marque
Springer
EAN papier
9783319994857
EAN PDF
9783319994864
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
26
Taille du fichier
4444 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
47,46 €
EAN EPUB
9783319994864
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
26
Taille du fichier
22487 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
47,46 €

Suggestions personnalisées