On an Initial Value Problem Describing the Small Oscillations of a Floating Cylinder

Abstract

We study a coupled PDE-ODE system modeling the small oscillations of a floating cylinder interacting with small water waves. We consider the case when the floating body is an infinite circular cylinder, so that the equations of the free surface of the fluid can be written in one space dimension. The governing equations are formulated as an abstract evolution equation in a suitable Hilbert space, and we establish the well-posedness of the associated initial value problem. A key element of the proof is the analysis of a partial Dirichlet-to-Neumann map on an unbounded domain with a non-smooth boundary.

arXiv commentThis work is funded by the European Union (Horizon Europe MSCA project ModConFlex, grant number 101073558). The second author acknowledges the support of the BOURGEONS project, grant ANR-23-CE40-0014-01 of the French National Research Agency (ANR)