Gravity water waves with constant nonzero vorticity γ and rational γ²/g admit smooth small-amplitude solutions whose high Sobolev norms grow arbitrarily large while low norms stay small.
On the wave turbulence theory of 2D gravity waves, II: propagation of randomness
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Rigorous derivation of the 4-wave kinetic equation for the full beta-FPUT system in the joint limit N to infinity and beta to zero under weakly nonlinear scalings, reaching times up to the kinetic timescale to the power 2/3, by directly incorporating non-resonant terms in a diagrammatic expansion.
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.
citing papers explorer
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Transfer of energy for pure-gravity water waves with constant vorticity
Gravity water waves with constant nonzero vorticity γ and rational γ²/g admit smooth small-amplitude solutions whose high Sobolev norms grow arbitrarily large while low norms stay small.
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Rigorous Derivation of the Wave Kinetic Equation for full $\beta$-FPUT System
Rigorous derivation of the 4-wave kinetic equation for the full beta-FPUT system in the joint limit N to infinity and beta to zero under weakly nonlinear scalings, reaching times up to the kinetic timescale to the power 2/3, by directly incorporating non-resonant terms in a diagrammatic expansion.
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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.