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Existence of the solutions for the Ginzburg–Landau equations of superconductivity in three spatial dimensions

Published online by Cambridge University Press:  14 November 2011

Bixiang Wang  and
Ning Su
Bixiang Wang
Affiliation:
Department of Applied Mathematics, Tsinghua University, Beijing 100084, Peoples Republic of China and Department of Mathematics, Brigham Young University, Provo, UT 84602, USA
Ning Su
Affiliation:
Department of Applied Mathematics, Tsinghua University, Beijing 100084, People's, Republic of China
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Abstract

The time-dependent Ginzburg-Landau equations of superconductivity in three spatial dimensions are investigated in this paper. We establish the existence of global weak solutions for this model with any Lp (p ≧ 3) initial data. This work generalizes the results of Wang and Zhan.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 3 , 1999 , pp. 627 - 639
Copyright
Copyright © Royal Society of Edinburgh 1999

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References

1Adams, R. A.. Sobolev spaces (New York: Academic, 1975).Google Scholar
2Chapman, S. J.. Macroscopic models of superconductivity. PhD thesis (Oxford University, 1992).Google Scholar
3Chen, Z. M., Hoffmann, K. H. and Liang, J.. On a non-stationary Ginzburg-Landau superconductivity model. Math. Meth. Appl. Sci. 16 (1993), 855–875.Google Scholar
4Du, Q.. Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau model for superconductivity. Appl. Analysis 53 (1994), 1–17.Google Scholar
5Frahm, H., Ullah, S. and Dorsey, A.. Flux dynamics and the growth of the superconducting phase. Phys. Rev. Lett. 66 (1991), 3067–3072.Google Scholar
6Girault, V. and Raviart, P. A.. Finite element methods for Naviei—Stokes equations (New York: Springer, 1986).CrossRefGoogle Scholar
7Gorkov, L. and Eliashberg, G.. Generalization of the Ginzburg-Landau equations for nonstationary problems in the case of alloys with paramagnetic impurities. Soviet Phys. JETP 27 (1968), 328–334.Google Scholar
8Lions, J. L.. Quelques methodes de resolution des problems auxlimites non lineaires (Paris: Dunrod, 1969).Google Scholar
9Machida, M. and Kaburaki, H.. Direct simulation of the time-dependent Ginzburg-Landau equation for type-II superconducting thin film: vortex dynamics and V–I characteristics. Phys. Rev. Lett. 71 (1993), 3206–3209.CrossRefGoogle ScholarPubMed
10Tang, Q.. On an evolutionary system of Ginzburg—Landau equations with fixed total magnetic flux. Commun. Partial Diff. Eqns 20 (1995), 1–36.Google Scholar
11Tang, Q. and Wang, S.. Time dependent Ginzburg-Landau equations of superconductivity. Physica D 88 1995, 139–166.Google Scholar
12Tinkham, M.. Introduction to superconductivity (New York: McGraw-Hill, 1975).Google Scholar
13Wang, B. and Wang, S.. Gevrey class regularity for the solutions of the Ginzburg–Landau equations of superconductivity. Discr. Cont. Dyn. Syst. 4 (1998), 507–522.Google Scholar
14Wang, S. and Zhan, M.. Lp solutions to the time dependence Ginzburg-Landau equations of superconductivity. The Institute for Scientific Computing and Applied Mathematics, Indiana University, Preprint no. 9622.Google Scholar
15Weinan, E.. Dynamics of vortices in Ginzburg–Landau theories with applications to superconductivity. Physica D 77 (1994), 383–404.Google Scholar