Calculus of Variations and Geometric Measure Theory
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F. Bethuel - G. Orlandi - D. Smets

Collisions and phase-vortex interactions in dissipative Ginzburg-Landau dynamics

created by orlandi on 26 Oct 2005
modified on 03 Dec 2005


Published Paper

Inserted: 26 oct 2005
Last Updated: 3 dec 2005

Journal: Duke Math. J.
Volume: 130
Number: 3
Pages: 523-614
Year: 2005


In this paper we describe a natural framework for the vortex dynamics in the parabolic complex Ginzburg-Landau equation in $R^2$. This general setting does not rely on any assumption of well-preparedness and has the advantage to be valid even after collision times. We analyze carefully collisions leading to annihilation. A new phenomenon is identified, the phase-vortex interaction, related to persistence of low frequency oscillations, and leading to an unexpected drift in the motion of vortices.

2000 Mathematics Subject Classification : 35B40, 35K55, 35Q40.

Keywords: parabolic equations, Ginzburg-Landau, vortex dynamics


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