ALAZARD, Thomas; MÉTIVIER, Guy

Metadatos

Mostrar el registro completo del ítem

Licencia de uso del documento

ALAZARD, Thomas
Laboratoire de Mathématiques d'Orsay [LMO]

MÉTIVIER, Guy
Institut de Mathématiques de Bordeaux [IMB]

Idioma

Article de revue

Este ítem está publicado en

Communications in Partial Differential Equations. 2009, vol. 34, n° 12, p. 1632-1704

Taylor & Francis

Resumen en inglés

This paper is concerned with a priori $C^\infty$ regularity for three-dimensional doubly periodic travelling gravity waves whose fundamental domain is a symmetric diamond. The existence of such waves was a long standing open problem solved recently by Iooss and Plotnikov. The main difficulty is that, unlike conventional free boundary problems, the reduced boundary system is not elliptic for three-dimensional pure gravity waves, which leads to small divisors problems. Our main result asserts that sufficiently smooth diamond waves which satisfy a diophantine condition are automatically $C^\infty$. In particular, we prove that the solutions defined by Iooss and Plotnikov are $C^\infty$. Two notable technical aspects are that (i) no smallness condition is required and (ii) we obtain an exact paralinearization formula for the Dirichlet to Neumann operator.< Leer menos

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190539

Proyecto ANR

Equations aux dérivées partielles dispersives - ANR-07-BLAN-0250

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251