A gradient flow approach to an evolution problem arising in superconductivity
A gradient flow approach to an evolution problem arising in superconductivity
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DOI：
10.1002/cpa.20223
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发表时间：
2008-11-01
影响因子：
3
通讯作者：
Serfaty, Sylvia
中科院分区：
文献类型：
--
作者：
Ambrosio, Luigi;Serfaty, Sylvia
我们研究了由Chapman， Rubinstein和Schatzman提出的演化方程，作为超导体中涡旋密度演化的平均场模型。我们处理有界区域的情况，其中漩涡可以进出该区域。我们证明了该方程可以严格地推导为由概率测度上的瓦瑟斯坦距离引起的黎曼结构的某些特定能量的梯度流。这导致我们得到一些存在唯一性结果和耗能恒等式。我们还展示了一些“熵”在流动中减少，并允许我们得到规律性的结果（从L-p开始的解，p >1，保持在L-p）。(C) 2007 Wiley期刊公司
We study an evolution equation proposed by Chapman, Rubinstein, and Schatzman as a mean-field model for the evolution of the vortex density in a superconductor. We treat the case of a bounded domain where vortices can exit or enter the domain. We show that the equation can be derived rigorously as the gradient flow of some specific energy for the Riemannian structure induced by the Wasserstein distance on probability measures. This leads us to some existence and uniqueness results and energy-dissipation identities. We also exhibit some "entropies" that decrease through the flow and allow us to get regularity results (solutions starting in L-p, p > 1, remain in L-p). (C) 2007 Wiley Periodicals, Inc.