Seminario di Fisica Matematica

Mercoledi' 26 giugno alle ore 14.30, il dott. Paolo Ventura (Universita' di Milano) terra' il seminario dal titolo "Infinitely many isolas of modulational instability for Stokes waves".


ABSTRACT: Stokes waves are the simplest nontrivial form of water waves, featuring a periodic profile moving steadily in one direction. In the 1970s, Benjamin and Feir discovered through experiments that the steady profile is unstable under long-wave perturbations, i.e. disturbances that, although small in amplitude, have much longer periods. In recent years, significant mathematical progress has been made on this 'modulational' instability, particularly in the linear approximation, which involves understanding the L2(R)-spectrum of the water wave operator linearized along a Stokes wave. I will present the latest results, specifically the full description of arbitrary portions of the unstable spectrum. As long conjectured by numerical investigations, this spectrum consists of infinitely many isolated elliptical branchings, called 'isolas', centered on the imaginary axis that become exponentially small as one moves away from the origin of the complex plane. This work was done in collaboration with M. Berti, L. Corsi, and A. Maspero.

Il seminario avrà luogo in presenza presso il Dipartimento di Matematica e Fisica
Lungotevere Dante 376 - Aula M4
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