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.
Long-time dynamics for the Kelvin–Helmholtz equations close to circular vortex sheets
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Proves sharp global rigidity of the unit circle for small Weber numbers in 2D hollow vortex free boundary problem, supporting Crowdy-Wegmann conjecture, plus isoperimetric-isocapacitary inequality and variational classification.
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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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Global rigidity of two-dimensional bubbles
Proves sharp global rigidity of the unit circle for small Weber numbers in 2D hollow vortex free boundary problem, supporting Crowdy-Wegmann conjecture, plus isoperimetric-isocapacitary inequality and variational classification.