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.
Long-time dynamics for the Kelvin–Helmholtz equations close to circular vortex sheets
2 Pith papers cite this work. Polarity classification is still indexing.
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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
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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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.