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- W4383469181 abstract "In this paper we consider three-dimensional steady water waves with vorticity, under the action of gravity and surface tension; in particular we consider so-called Beltrami flows, for which the velocity field and the vorticity are collinear. We discuss a recent variational formulation of the problem which involves a generalisation of the classical Dirichlet-Neumann operator. We study this operator in detail, extending some well-known results for the classical Dirichlet-Neumann operator, such as the Taylor expansion in homogeneous powers of the wave profile, the computation of its differential and the asymptotic expansion of its associated symbol. A new formulation of the problem as a single equation for the wave profile is also presented and discussed in a similar vein. As an application of these results we rigorously prove existence of doubly periodic gravity-capillary steady waves and construct approximate doubly periodic gravity steady waves." @default.
- W4383469181 created "2023-07-07" @default.
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- W4383469181 date "2023-07-04" @default.
- W4383469181 modified "2023-10-18" @default.
- W4383469181 title "Analytical Study of a generalised Dirichlet-Neumann operator and application to three-dimensional water waves on Beltrami flows" @default.
- W4383469181 doi "https://doi.org/10.48550/arxiv.2307.01702" @default.
- W4383469181 hasPublicationYear "2023" @default.
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