Acta Mathematica Sinica

, Volume 22, Issue 6, pp 1831–1842

Ginzburg–Landau Vortex and Mean Curvature Flow with External Force Field



This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a parabolic Ginzburg–Landau system which simulates inhomogeneous type II superconducting materials and three–dimensional superconducting thin films having variable thickness. We will prove that the vortex of the problem is moved by a codimension k mean curvature flow with external force field. Besides, we will show that the mean curvature flow depends strongly on the external force, having completely different phenomena from the usual mean curvature flow.


system of parabolic equations Ginzburg–Landau vortex mean curvature flow 

MR (2000) Subject Classification

35K55 35K65 35J60 52C44 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijing 100084P. R. China

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