Linear water waves and freely floating bodies: the Fritz John model

Abstract:

The F. John problem is a linear model describing the interaction between an incompressible, irrotational free-surface fluid and a partially immersed, freely floating body. Introduced by F. John in 1949, it is closely related to the Cummins equations, which are widely used in naval engineering to describe wave–structure interactions. Its rigorous analysis is subtle because the contact points between the free surface and the body create corners in the fluid domain. The resulting corner singularities lead to a non-standard trace space for the velocity potential and must be incorporated into the mathematical formulation of the problem.

In this talk, I will present recent work in collaboration with David Lannes. I will explain how the model for floating bodies is derived, how the geometry near the contact points affects the fluid motion, and why these effects matter for the analysis and numerical modelling of wave–structure interactions.