Generation of vortices in the Ginzburg-Landau heat flow

Michał Kowalczyk; Xavier Lamy

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arXiv · 2211.15773

Generation of vortices in the Ginzburg-Landau heat flow

Michał Kowalczyk·Xavier Lamy

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Abstract

We consider the Ginzburg-Landau heat flow on the two-dimensional flat torus, starting from an initial data with a finite number of nondegenerate zeros -- but possibly very high initial energy. We show that the initial zeros are conserved and the flow rapidly enters a logarithmic energy regime, from which the evolution of vortices can be described by the works of Bethuel, Orlandi and Smets.

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Michał Kowalczyk, Xavier Lamy. 2022-11-28. Generation of vortices in the Ginzburg-Landau heat flow. https://arxiv.org/abs/2211.15773

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