The system will be going down for regular maintenance. Please save your work and logout.
Paralinearization of the Dirichlet to Neumann operator
Language
en
Article de revue
This item was published in
Communications in Partial Differential Equations. 2009, vol. 34, p. 1634--1704
Taylor & Francis
English Abstract
This paper is concerned with {\em 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 ...Read more >
This paper is concerned with {\em 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.Read less <
Origin
Hal imported