Abstract
In this work, we prove the global well-posedness of strong solutions to a non-isothermal model for superconductivity in a three-dimensional domain.
Similar content being viewed by others
References
Phillips, D., Shin, E.: On the analysis of a non-isothermal model for superconductivity. Eur. J. Appl. Math. 15, 147–179 (2004)
Guo, B., Yuan, G.: Cauchy problem for the Ginzburg–Landau equation for the superconductivity model. Proc. R. Soc. Edinb. Sect. A Math. 127, 1181–1192 (1997)
Akiyama, T., Kasai, H., Tsutsumi, M.: On the existence of the solution of the time dependent Ginzburg–Landau equations in \({\mathbb{R}}\). Funkc. Ekvacioj 43, 255–270 (2000)
Fan, J., Jiang, S.: Global existence of weak solutions of a time-dependent 3-D Ginzburg–Landau model for superconductivity. Appl. Math. Lett. 16, 435–440 (2003)
Chen, Z.M., Elliott, C., Tang, Q.: Justification of a two-dimensional evolutionary Ginzburg–Landau superconductivity model. RAIRO Model Math. Anal. Numer. 32, 25–50 (1998)
Chen, Z.M., Hoffmann, K.H., Liang, J.: On a nonstationary Ginzburg–Landau superconductivity model. Math. Methods Appl. Sci. 16, 855–875 (1993)
Du, Q.: Global existence and uniqueness of solutions of the time dependent Ginzburg–Landau model for superconductivity. Appl. Anal. 52, 1–17 (1994)
Tang, Q.: On an evolutionary system of Ginzburg–Landau equations with fixed total magnetic flux. Commun. PDE 20, 1–36 (1995)
Tang, Q., Wang, S.: Time dependent Ginzburg–Landau equation of superconductivity. Physica D 88, 139–166 (1995)
Fan, J., Ozawa, T.: Global well-posedness of weak solutions to the time-dependent Ginzburg–Landau model for superconductivity. Taiwan. J. Math. 22(4), 851–858 (2018)
Fan, J., Samet, B., Zhou, Y.: Uniform regularity for a 3D time-dependent Ginzburg–Landau model in superconductivity. Comput. Math. Appl. 75, 3244–3248 (2018)
Fan, J., Gao, H., Guo, B.: Uniqueness of weak solutions to the 3D Ginzburg–Landau superconductivity model. Int. Math. Res. Not. 2015(5), 1239–1246 (2015)
Fan, J., Gao, H.: Uniqueness of weak solutions in critical spaces of the 3-D time-dependent Ginzburg–Landau equations for superconductivity. Math. Nachr. 283, 1134–1143 (2010)
Al Baba, H.: Maximal \(L^p-L^q\) regularity to the Stokes problem with Navier boundary conditions. arXiv: 1605.05318
Al Baba, H., Amrouche, C., Escobedo, M.: Semigroup theory for the Stokes operator with Navier-type boundary conditions on \(L^p\)-spaces. arXiv: 1601.06019
Acknowledgements
The authors are grateful to the referees and the editors whose comments and suggestions greatly improved the presentation of this paper. Jishan Fan is partially supported by NSFC (Nos. 11971234, 11171154). Tong Tang is partially supported by NSFC (No. 11801138).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Yong Zhou.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Fan, J., Jing, L., Nakamura, G. et al. A Note on a Non-isothermal Model for Superconductivity. Bull. Malays. Math. Sci. Soc. 43, 3027–3034 (2020). https://doi.org/10.1007/s40840-019-00852-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40840-019-00852-3