On the stability of a singular vortex dynamics

Abstract

In this paper we address the question of the singular vortex dynamics exhibited in [15], which generates a corner in finite time. The purpose is to prove that under some appropriate small regular perturbation the corner still remains. Our approach uses the Hasimoto transform and deals with the long range scattering properties of a Gross-Pitaevski equation with time-variable coefficients.

35 pages, revised version, to appear in Comm. Math. Phys

References in corpus (2)

• Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions
• On the Dirac delta as initial condition for nonlinear Schrödinger equations

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• Recent results for the Landau-Lifshitz equation
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• Gradient catastrophe and flutter in vortex filament dynamics