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Stability of vortex rings in a model of superflow. (English) Zbl 0791.35128
Summary: Stability of an isolated vortex ring is studied in the framework of the Ginzburg-Landau model using the nonlocal equation of motion. It is shown that an instability which might have been caused by nonlocal effects in the long-scale theory falls into the range of wavelengths comparable with the healing length. A higher-order effect of acoustic emission is found to play a stabilizing role, since the dissipation of the energy of perturbations by isotropic emission is sufficiently strong to restore the circular shape with only a small loss of the momentum.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
76B47 Vortex flows for incompressible inviscid fluids
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