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

Séminaire « Analyse numérique et équations aux dérivées partielles »
Salle de réunion M2

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.

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