Massimiliano Berti, Alberto Maspero, Federico Murgante
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Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves
We present the almost global in time existence result in [13]
of small amplitude space periodic
solutions of the 1D gravity-capillary water waves equations with constant vorticity
and we describe the ideas of proof.
This is based on a novel Hamiltonian paradifferential
Birkhoff normal form approach for quasi-linear PDEs.
期刊介绍：
Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
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