Afficher la notice abrégée

dc.contributor.authorBuffoni, Boris
dc.contributor.authorSéré, Eric
dc.contributor.authorToland, John
dc.date.accessioned2011-05-13T08:11:56Z
dc.date.available2011-05-13T08:11:56Z
dc.date.issued2003
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6276
dc.language.isoenen
dc.subjectperiodic water wavesen
dc.subjectfree-boundary problemen
dc.subjectvariational methoden
dc.subjectcritical-point theoryen
dc.subjectsaddle pointen
dc.subjectmountain passen
dc.subjectMorse indexen
dc.subject.ddc515en
dc.titleSurface water waves as saddle points of the energyen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenBy applying the mountain-pass lemma to an energy functional, we establish the existence of two-dimensional water waves on the surface of an infinitely deep ocean in a constant gravity field. The formulation used, which is due to K. I. Babenko [3, 4] (and later to others, independently), has as its independent variable an amplitude function which gives the surface elevation. Its nonlinear term is purely quadratic but it is nonlocal because it involves the Hilbert transform. Moreover the energy functional from which it is derived is rather degenerate and offers an important challenge in the calculus of variations. In the present treatment the first step is to truncate the integrand, and then to penalize and regularize it. The mountain-pass lemma gives the existence of critical points of the resulting problem. To check that, in the limit of vanishing regularization, the critical points converge to a non-trivial water wave, we need a priori estimates and information on their Morseindex in the spirit of the work by Amann and Zehnder [1] (see also [14]). The amplitudes of the waves so obtained are compared with those obtained from the bifurcation argument of Babenko, and are found to extend the parameter range where existence is known by analytical methods. We also compare our approach with the minimization-under-constraint method used by R. E. L. Turner [25].en
dc.relation.isversionofjnlnameCalculus of Variations and Partial Differential Equations
dc.relation.isversionofjnlvol17en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2003
dc.relation.isversionofjnlpages199-220en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00526-002-0166-9en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAnalyseen


Fichiers attachés à cette notice

Thumbnail
Thumbnail

Ce document fait partie de la (des) collection(s) suivante(s)

Afficher la notice abrégée