Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves
| hal.structure.identifier | Laboratoire de Mathématiques d'Orsay [LMO] | |
| dc.contributor.author | ALAZARD, Thomas | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MÉTIVIER, Guy | |
| dc.date.accessioned | 2024-04-04T02:34:17Z | |
| dc.date.available | 2024-04-04T02:34:17Z | |
| dc.date.issued | 2009 | |
| dc.identifier.issn | 0360-5302 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190539 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Equations aux dérivées partielles dispersives - ANR-07-BLAN-0250 | |
| dc.language.iso | en | |
| dc.publisher | Taylor & Francis | |
| dc.title.en | Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 0901.2888 | |
| bordeaux.journal | Communications in Partial Differential Equations | |
| bordeaux.page | 1632-1704 | |
| bordeaux.volume | 34 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 12 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00354473 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00354473v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20in%20Partial%20Differential%20Equations&rft.date=2009&rft.volume=34&rft.issue=12&rft.spage=1632-1704&rft.epage=1632-1704&rft.eissn=0360-5302&rft.issn=0360-5302&rft.au=ALAZARD,%20Thomas&M%C3%89TIVIER,%20Guy&rft.genre=article |
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