Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 10
Submit an article Journal homepage
52
Views
0
CrossRef citations to date
0
Altmetric
Articles

Global well-posedness of axially symmetric weak solutions to the Ginzburg–Landau model in superconductivity

Shengqi Lua Department of Mathematics and Physics, Sanjiang University, Nanjing, People's Republic of ChinaView further author information
,
Miaochao Chenb School of Mathematics and Statistics, Chaohu University, Hefei, People's Republic of ChinaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-6003-9033View further author information
ORCID Icon &
Qilin Liuc School of Mathematics, Southeast University, Nanjing, People's Republic of ChinaView further author information
Pages 2163-2169 | Received 27 Feb 2019, Accepted 08 Oct 2019, Published online: 18 Oct 2019

References

  • Chen ZM, Elliott C, Tang Q. Justification of a two-dimensional evolutionary Ginzburg–Landau superconductivity model. RAIRO Model Math Anal Numer. 1998;32:25–50. doi: 10.1051/m2an/1998320100251
  • Chen ZM, Hoffmann KH, Liang J. On a nonstationary Ginzburg–Landau superconductivity model. Math Methods Appl Sci. 1993;16:855–875. doi: 10.1002/mma.1670161203
  • Du Q. Global existence and uniqueness of solutions of the time dependent Ginzburg–Landau model for superconductivity. Appl Anal. 1994;52:1–17. doi: 10.1080/00036819408840240
  • Tang Q. On an evolutionary system of Ginzburg–Landau equations with fixed total magnetic flux. Commun Partial Differ Equ. 1995;20:1–36.
  • Tang Q, Wang S. Time dependent Ginzburg–Landau equation of superconductivity. Physica D. 1995;88:139–166. doi: 10.1016/0167-2789(95)00195-A
  • Fan J, Jiang S. Global existence of weak solutions of a time-dependent 3-D Ginzburg–Landau model for superconductivity. Appl Math Lett. 2003;16:435–440. doi: 10.1016/S0893-9659(03)80069-1
  • Fan J, Ozawa T. Uniqueness of weak solutions to the Ginzburg–Landau model for superconductivity. Z Angew Math Phys. 2012;63:453–459. doi: 10.1007/s00033-011-0164-x
  • Fan J, Gao H, Guo B. Uniqueness of weak solutions to the 3D Ginzburg–Landau superconductivity model. Int Math Res Notices. 2015;5:1239–1246. doi: 10.1093/imrn/rnt253
  • Fan J, Gao H. Uniqueness of weak solutions in critical spaces of the 3-D time-dependent Ginzburg–Landau equations for superconductivity. Math Nachr. 2010;283:1134–1143. doi: 10.1002/mana.200710083
  • Guo B, Yuan G. Cauchy problem for the Ginzburg–Landau equation for the superconductivity model. Proc R Soc Edinburgh: Sect A Math. 1997;123:1181–1192. doi: 10.1017/S0308210500027001
  • Rodriguez-Bernal A, Wang B. Cauchy problem for the time-dependent Ginzburg–Landau model of superconductivity. Proc R Soc Edinburgh: Sect A Math. 2000;130:1383–1404. doi: 10.1017/S0308210500000731
  • Akiyama T, Kasai H, Tsutsumi M. On the existence of the solution of the time dependent Ginzburg–Landau equations in R3. Funkcialaj Ekvacioj. 2000;43:255–270.
  • Kato T. Strong Lp-solutions of the Navier–Stokes equation in Rm with applications to weak solutions. Math Z. 1984;187:471–480. doi: 10.1007/BF01174182

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.