Hamiltonian Birkhoff normal form for gravity-capillary water waves with constant vorticity: almost global existence

Periodic solutions to PDEs (35B10) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Capillarity (surface tension) for incompressible inviscid fluids (76B45) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Free boundary problems for PDEs (35R35) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

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