Smooth small solutions to gravity water waves with constant vorticity show arbitrary growth in high Sobolev norms, proving energy transfer to high frequencies and weak turbulence while the flow remains smooth.
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math.AP 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
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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Transfer of energy for pure-gravity water waves with constant vorticity
Smooth small solutions to gravity water waves with constant vorticity show arbitrary growth in high Sobolev norms, proving energy transfer to high frequencies and weak turbulence while the flow remains smooth.
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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.