Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature

• 成果类型: Article
• 署名作者: Bethuel, F.; Orlandi, G.; Smets, D.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.163.37
• 发表日期: 2006
• 页码: 37-163
• 关键词: quantization property; HARMONIC MAPS; vortices; DYNAMICS; FLOW; interfaces; EXISTENCE; varifold; SURFACES; spheres

摘要

For the complex parabolic Ginzburg-Landau equation, we prove that, asymptotically, vorticity evolves according to motion by mean curvature in Brakke's weak formulation. The only assumption is a natural energy bound on the initial data. In some cases, we also prove convergence to enhanced motion in the sense of Ilmanen.