For almost all Weber numbers below 4(2+sqrt(3)), small-amplitude circular vortex sheets with surface tension stay O(ε)-close to the circular equilibrium for times of order ε^{-(N+1)} for every integer N.
Ambrose and Nader Masmoudi
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Long-time dynamics for the Kelvin-Helmholtz equations close to circular vortex sheets
For almost all Weber numbers below 4(2+sqrt(3)), small-amplitude circular vortex sheets with surface tension stay O(ε)-close to the circular equilibrium for times of order ε^{-(N+1)} for every integer N.