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.
M.,Finite-time singularity formation forC1,αsolutions to the incompressible Euler equations onR3, Annals of Mathematics, 194(3), 647-727, 2021
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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.