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Formation of singularities and self-similar vortex motion under the localized induction approximation. (English) Zbl 1044.35089
The dynamical behaviour of an isolated vortex filament in three dimensions is studied. A solution is constructed explicitly in terms of the curvature of the initial regular configuration.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
76B47 Vortex flows for incompressible inviscid fluids
35A21 Singularity in context of PDEs
35K45 Initial value problems for second-order parabolic systems
35Q35 PDEs in connection with fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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