, Volume 22, Issue 6, pp 1831-1842
Date: 14 Mar 2006

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

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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.

Supported by National 973–Project and Basic Research Grant of Tsinghua University