Two-dimensional water waves with constant vorticity and general bottom topography

2025/05/08 by Pasquali, S.
#37K45 #76B03 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.05430

Abstract

In this paper we consider two-dimensional water waves with constant vorticity, under the action of gravity and surface tension, in a fluid domain with finite depth and general bottom topography. We present a formulation which generalizes the one by Zakharov-Craig-Sulem for irrotational water waves, and the one by Constantin-Ivanov-Prodanov for water waves with constant vorticity and flat bottom topography. We study in detail an operator which appears in such formulation, extending well-known results for the classical Dirichlet-Neumann operator, such as an analiticity result, the Taylor expansion in homogeneous powers of the wave profile, and a paralinearization formula. As an application, we prove a local well-posedness result.

Citations

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• Stokes waves with vorticity