Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - E. Mainini - S. Serfaty

Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices

created by mainini on 18 Mar 2010
modified on 26 Mar 2011


Published Paper

Inserted: 18 mar 2010
Last Updated: 26 mar 2011

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Volume: 28
Number: 2
Pages: 217-246
Year: 2011


We study of the Chapman-Rubinstein-Schatzman evolution model for superconductivity, viewed as a gradient flow on the space of measures equipped with the quadratic Wasserstein structure. We consider general signed measures, as in the physical model. Understanding the evolution as a gradient flow in this context gives rise to several new questions, in particular how to define a ``Wasserstein" distance for signed measures. We generalize the minimizing movement scheme in this context, we show that the one step regularity estimates hold as in the positive case, and derive an evolution equation for the measure which contains an error term compared to the Chapman-Rubinstein-Schatzman model. Moreover, we also show the same applies to a very similar dissipative model on the whole plane.


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