Estimate for a solution to the water wave problem in the presence of a submerged body

TL;DR

This paper derives explicit bounds for linear water wave solutions in deep water with a submerged body, considering geometric constraints, advancing understanding of wave behavior in complex submerged environments.

Contribution

It provides a new explicit bound for water wave solutions accounting for domain geometry and source functions, enhancing analytical tools for submerged body problems.

Findings

Explicit bounds depend on domain geometry and source functions

Results applicable to deep water wave propagation with submerged objects

Improves analytical understanding of wave solutions in complex geometries

Abstract

We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the functions on the right-hand side.