Vortices in a stochastic parabolic Ginzburg-Landau equation

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• 作者：Olga Chugreeva ; Christof Melcher
• 关键词：Stochastic Ginzburg ; Landau equation ; Multiplicative noise ; Stochastic Ginzburg ; Landau vortices
• 刊名：Stochastics and Partial Differential Equations: Analysis and Computations
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：5
• 期：1
• 页码：113-143
• 全文大小：
• 刊物主题：Probability Theory and Stochastic Processes; Partial Differential Equations; Statistical Theory and Methods; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Nu
• 出版者：Springer US
• ISSN：2194-041X
• 卷排序：5

文摘

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.