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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China

    Huai Yu Jian & Yan Nan Liu

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  1. Huai Yu Jian
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  2. Yan Nan Liu
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Correspondence to Huai Yu Jian.

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

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Jian, H.Y., Liu, Y.N. Ginzburg–Landau Vortex and Mean Curvature Flow with External Force Field. Acta Math Sinica 22, 1831–1842 (2006). https://doi.org/10.1007/s10114-005-0698-y

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