Speaker: Alberto Maspero, Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Date: April 13, 2023
Title: Full description of Benjamin-Feir instability of Stokes waves in finite depth: Part I
Abstract: Stokes waves, which are small amplitude space periodic solutions of 2D gravity water waves, are unstable to long-wave perturbations, as Benjamin and Feir predicted in 1967. This is the first of a series of two seminars in which we state and prove the complete Benjamin-Feir linear instability of the Stokes waves in finite depth, as well as deep waters. We completely describe the behavior of the four eigenvalues close to zero of the linearized equations at the Stokes wave, as the Floquet exponent is turned on. We prove in particular the conjecture that a pair of non-purely imaginary eigenvalues depicts a closed figure eight, parameterized by the Floquet exponent, in full agreement with numerical simulations. This is a joint work with M. Berti and P. Ventura.
Location: Residents of Lewis Hall can attend talks in the Wan Conference Room (Lewis 208). The talk will also be streamed live via Zoom.