Uniqueness of weak solutions of time-dependent 3-D Ginzburg-Landau model for superconductivity

Jishan Fan; Hongjun Gao

doi:10.1007/s11464-007-0013-6

Front. Math. China ›› 2007, Vol. 2 ›› Issue (2) : 183 -189. DOI: 10.1007/s11464-007-0013-6

Research Article

Uniqueness of weak solutions of time-dependent 3-D Ginzburg-Landau model for superconductivity

Jishan Fan ¹
, Hongjun Gao ²^,^b

Author information +

History +

PDF (132KB)

Abstract

We prove the uniqueness of weak solutions of the time-dependent 3-D Ginzburg-Landau model for superconductivity with (Ψ₀, A₀) ∈ L²(Ω) initial data under the hypothesis that (Ψ, A) ∈ C([0, T]; L³(Ω)) using the Lorentz gauge.

Keywords

uniqueness / Ginzburg-Landau model / superconductivity / Lorentz gauge

Cite this article

Download citation ▾

Jishan Fan, Hongjun Gao. Uniqueness of weak solutions of time-dependent 3-D Ginzburg-Landau model for superconductivity. Front. Math. China, 2007, 2(2): 183-189 DOI:10.1007/s11464-007-0013-6

登录浏览全文

4963

注册一个新账户忘记密码

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Chen Z. M., Elliott C., Tang Q. Justification of a two-dimensional evolutionary Ginzburg-Landau superconductivity model, RAIRO Model. Math Anal Numer, 1998, 32: 25-50.

[2]	Chen Z. M., Hoffmann K. H., Liang J. On a nonstationary Ginzburg-Landau superconductivity model. Math Meth Appl Sci, 1993, 16: 855-875.

[3]	Tang Q. On an evolutionary system of Ginzburg-Landau equations with fixed total magnetic flux. Comm PDE, 1995, 20: 1-36.

[4]	Du Q. Global existence an uniqueness of solutions of the time-dependent Ginzburg-Landau model for superconductivity. Appl Anal, 1994, 521: 1-17.

[5]	Liang J. The regularity of solutions for the curl boundary problems and Ginzburg-Landau superconductivity model. Math Model Meth Appl Sci, 1995, 5: 528-542.

[6]	Tang Q., Wang S. Time dependent Ginzburg-Landau equation of superconductivity. Physica D, 1995, 88: 139-166.

[7]	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.

[8]	Zaouch F. Time-periodic solutions of the time-dependent Ginzburg-Landau equations of surperconductivity. Z Angew Math Phys, 2003, 54: 905-918.

[9]	Phillips D., Shin E. On the analysis of a non-isothermal model for superconductivity. Euro J Appl Math, 2004, 15: 147-179.

[10]	Chen Z. M., Hoffmann K. H. Global classical solutions to a non-isothermal dynamical Ginzburg-Landau model in superconductivity. Numer Funct Anal Optimiz, 1997, 18: 901-920.

[11]	Wang B. X. Uniqueness of solutions for the Ginzburg-Landau model of superconductivity in three spatial dimensions. J Math Anal Appl, 2002, 266: 1-20.