For almost all surface tensions, small 3D gravity-capillary water wave solutions exist and stay small up to quadratic times ε^{-2} via a quasi-resonant normal form on selected frequency scales.
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Quasi-resonant normal form and quadratic lifespan for 3D gravity-capillary water waves
For almost all surface tensions, small 3D gravity-capillary water wave solutions exist and stay small up to quadratic times ε^{-2} via a quasi-resonant normal form on selected frequency scales.