# American Institute of Mathematical Sciences

September  2002, 1(3): 327-340. doi: 10.3934/cpaa.2002.1.327

## The global minimizers and vortex solutions to a Ginzburg-Landau model of superconducting films

 1 Department of Mathematics, South China Normal University, Guangzhou, Guangdong 510631, China 2 Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Received  June 2001 Revised  December 2001 Published  June 2002

In this paper, we discuss the global minimizers of a free energy for the superconducting thin films placed in a magnetic field $h_{e x}$ below the lower critical field $H_{c1}$ or between $H_{c1}$ and the upper critical field $H_{c2}$. For $h_{e x}$ is near but smaller than $H_{c1}$, we prove that the global minimizer having no vortex is unique. For $H_{c1}$<<$h_{e x}$<<$H_{c2}$, we prove that the density of the vortices of the global minimizer is proportional to the applied field.
Citation: Shijin Ding, Qiang Du. The global minimizers and vortex solutions to a Ginzburg-Landau model of superconducting films. Communications on Pure & Applied Analysis, 2002, 1 (3) : 327-340. doi: 10.3934/cpaa.2002.1.327
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