Scattering of water waves around a partially immersed obstacle

We study linear water waves in two dimensions in a fluid of infinite depth containing a fixed, partially immersed obstacle. Under natural geometric assumptions on the wetted boundary, we construct the harmonic lifting and prove that the associated Dirichlet-to-Neumann operator is nonnegative. This yields global wellposedness and conservation of energy. We establish the absence of trapped modes and, by a compact perturbation argument, a limiting absorption principle at every positive spectral parameter. Consequently, for all finite energy initial data in the physical local energy tends to zero as \(|t|\to \infty \), including in neighbourhoods of the obstacle and the contact points. Quantitative resolvent estimates and fractional regularity in the spectral parameter yield algebraic local energy decay. The obtained decay rate is not claimed to be optimal.