Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-30T23:27:30.940Z Has data issue: false hasContentIssue false
  • English
  • Français

Cauchy problem for the Ginzburg-Landau equation for the superconductivity model

Published online by Cambridge University Press:  14 November 2011

Boling Guo  and
Guangwei Yuan
Boling Guo
Affiliation:
Laboratory of Computational Physics, Centre for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, China
Guangwei Yuan
Affiliation:
Laboratory of Computational Physics, Centre for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, China
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper, the existence and uniqueness of the global smooth solution are proved for an evolutionary Ginzburg–Landau model for superconductivity under the Coulomb and Lorentz gauge.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 6 , 1997 , pp. 1181 - 1192
Copyright
Copyright © Royal Society of Edinburgh 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Chapman, S. J., Howison, S. D. and Ockendon, J. R.. Macroscopic models for superconductivity. SIAM Rev. 34 (1994), 529–60.Google Scholar
2Chen, Z. M., Hoffmann, K. H. and Liang, J.. On a non-stationary Ginzburg–Landau superconductivity model. Math. Meth. Appl. Sci. 16 (1993), 855–76.Google Scholar
3Colin, T.. On the Cauchy problem for a nonlocal nonlinear Schödinger equation occurring in plasma physics. Differential and Integral Equations 6 (1993), 1431–50.Google Scholar
4Du, Qiang. Global existence and uniqueness of solutions of the time-dependent Ginzburg–Landau model for superconductivity. Appl. Anal. 52 (1994), 1–17.Google Scholar
5Gor'kov, L. P. and Éliashberg, G. M.. Generalization of the Ginzburg–Landau equations for nonstationary problems in the case of alloys with paramagnetic impurities. Soviet Phys. JETP 27 (1968), 328–34.Google Scholar
6Stein, E. M.. Singular Integrals and Differentiability Properties of Functions (Princeton, NJ: Princeton University Press, 1970).Google Scholar
7Tang, Qi and Wang, Shouhong. Time-dependent Ginzburg–Landau equations of superconductivity (Preprint).Google Scholar
8Yang, Y.. Existence, regularity, and asymptotic behavior of the solutions to the Ginzburg–Landau equations on R 3. Comm. Math. Phys. 123 (1989), 147–61.Google Scholar
9Yang, Y.. The existence of Ginzburg–Landau solutions on the plane by a direct variational method. Ann. Inst. H. Poincaré, Anal. Non Linéaire 11 (1994), 517–36.Google Scholar