Spectral gaps for linearized water waves above a small periodic bottom. (Matthieu Ménard, Université Libre de Bruxelles)

We consider the movement of a free surface of a two-dimensional fluid over a variable bottom. We assume that the bottom has a periodic profile, and we study the water wave system linearized near equilibrium.  The latter reduces to a spectral problem for a Dirichlet–Neumann operator. We show that the spectrum of this operator consists of a series of bands separated by spectral gaps, which are zones of forbidden energies. This is a joint work with Christophe Lacave and Catherine Sulem.