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Dynamics of Water Waves

Hamiltonian systems, from topology to applications through analysis I October 08, 2018 - October 12, 2018

October 10, 2018 (10:30 AM PDT - 11:30 AM PDT)
Speaker(s): Massimiliano Berti (International School for Advanced Studies (SISSA/ISAS))
Location: MSRI: Simons Auditorium
Tags/Keywords
  • water waves

  • KAM for PDEs

  • Birkhoff normal form

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Abstract

I shall present recent results about the complex dynamics of the water waves equations of a bi-dimensional fluid under the action of gravity and eventually capillary forces, with space periodic boundary conditions. This is an infinite dimensional Hamiltonian system. We shall discuss both long time existence results as well as bifurcation of small amplitude time quasi-periodic solutions. Major difficulties are the quasi-linear nature of the water waves equations and complex resonance phenomena.

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