Wednesday 03 November 2021
11:30
Aula Volterra
abstract:
Small-amplitude, traveling, space periodic solutions -- called Stokes waves -- of the 2 dimensional gravity water waves equations in deep water are linearly unstable with respect to long-wave perturbations, as predicted by Benjamin and Feir in 1967. 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. Joint wotk with A. Maspero and P. Ventura.
il seminario si terrà in modalità mista.
Tutti gli interessati a partecipare in presenza devono contattare per email il prof. Andrea Malchiodi (andrea.malchiodi@sns.it).