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Vortices in a stochastic parabolic Ginzburg-Landau equation

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Abstract

We consider the variant of a stochastic parabolic Ginzburg-Landau equation that allows for the formation of point defects of the solution. The noise in the equation is multiplicative of the gradient type. We show that the family of the Jacobians associated to the solution is tight on a suitable space of measures. Our main result is the characterization of the limit points of this family. They are concentrated on finite sums of delta measures with integer weights. The point defects of the solution coincide with the points at which the delta measures are centered.

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Acknowledgments

We would like to thank anonymous referees for their comments which helped to improve the manuscript. This work contains some results from the PhD thesis [13] of the first author. The first author has been supported by the German Academic Exchange Service (DAAD) Grant A/10/86352.

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Authors and Affiliations

  1. Lehrstuhl I für Mathematik, RWTH Aachen University, Pontdriesch 14-16, 52056, Aachen, Germany

    Olga Chugreeva

  2. Lehrstuhl I für Mathematik & JARA Fundamentals of Future Information Technologies, RWTH Aachen University, Pontdriesch 14-16, 52056, Aachen, Germany

    Christof Melcher

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  1. Olga Chugreeva
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  2. Christof Melcher
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Correspondence to Olga Chugreeva.

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Chugreeva, O., Melcher, C. Vortices in a stochastic parabolic Ginzburg-Landau equation. Stoch PDE: Anal Comp 5, 113–143 (2017). https://doi.org/10.1007/s40072-016-0083-0

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  • DOI: https://doi.org/10.1007/s40072-016-0083-0

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