Speaker Massimiliano Berti, Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Date: April 20, 2023
Title: Full description of Benjamin-Feir instability of Stokes waves in finite depth: Part II
Abstract: In this talk I will provide complete proofs of the Benjamin-Feir instability result of Stokes waves described in the first seminar by A. Maspero, i.e. small amplitude space periodic solutions of 2D gravity water waves are unstable when subject to long-wave perturbations. We completely describe the behavior of the four eigenvalues close to zero of the linearized equations at the Stokes wave, both in finite and infinite depth, 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.