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Applicable Analysis
An International Journal
Volume 53, 1994 - Issue 1-2
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Original Articles

Global existence and uniqueness of solutions of the time-dependent ginzburg-landau model for superconductivity

Qiang Du Department of Mathematics,, Michigan State University, Lansing, USA
Pages 1-17 | Received 12 Jan 1993, Published online: 02 May 2007

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Shengqi Lu, Miaochao Chen & Qilin Liu. (2021) Global well-posedness of axially symmetric weak solutions to the Ginzburg–Landau model in superconductivity. Applicable Analysis 100:10, pages 2163-2169.
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Jishan Fan & Tohru Ozawa. (2016) Weak solutions to the Ginzburg-Landau model in superconductivity with the temporal gauge. Applicable Analysis 95:9, pages 2029-2038.
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Chaoxia Yang. (2014) Convergence of linearized backward Euler–Galerkin finite element methods for the time-dependent Ginzburg–Landau equations with temporal gauge. International Journal of Computer Mathematics 91:7, pages 1507-1515.
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K.-H. Hoffmann & Jun Zou. (1997) Finite element analysis on the lawrence-doniach model for layered superconductors. Numerical Functional Analysis and Optimization 18:5-6, pages 567-589.
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Articles from other publishers (88)

Zhiyong Si. (2024) A generalized scalar auxiliary variable method for the time-dependent Ginzburg-Landau equations. Acta Mathematica Scientia 44:2, pages 650-670.
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Limin MaZhonghua Qiao. (2023) An Energy Stable and Maximum Bound Principle Preserving Scheme for the Dynamic Ginzburg–Landau Equations under the Temporal Gauge. SIAM Journal on Numerical Analysis 61:6, pages 2695-2717.
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Yunxia Wang & Zhiyong Si. (2023) A convex splitting method for the time-dependent Ginzburg-Landau equation. Numerical Algorithms.
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Takeshi Mizushima & Masahiro Sato. (2023) Imprinting spiral Higgs waves onto superconductors with vortex beams. Physical Review Research 5:4.
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Huadong Gao & Wen Xie. (2023) A Finite Element Method for the Dynamical Ginzburg–Landau Equations under Coulomb Gauge. Journal of Scientific Computing 97:1.
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Erhan Coskun. (2023) On the numerical stability and transitional stages of time-dependent Ginzburg–Landau model of superconductivity. Physica A: Statistical Mechanics and its Applications 626, pages 129036.
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Dan Wang, Meng Li & Yu Lu. (2023) Unconditionally convergent and superconvergent analysis of second-order weighted IMEX FEMs for nonlinear Ginzburg-Landau equation. Computers & Mathematics with Applications 146, pages 84-105.
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Huadong GaoWeiwei Sun. (2023) Optimal Analysis of Non-Uniform Galerkin-Mixed Finite Element Approximations to the Ginzburg–Landau Equations in Superconductivity. SIAM Journal on Numerical Analysis 61:2, pages 929-951.
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Huoyuan Duan & Qiuyu Zhang. (2022) Residual-Based a Posteriori Error Estimates for the Time-Dependent Ginzburg–Landau Equations of Superconductivity. Journal of Scientific Computing 93:3.
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T. Okugawa, S. Park, P. Recher & D. M. Kennes. (2022) Vortex control in superconducting Corbino geometry networks. Physical Review B 106:2.
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T. Okugawa, A. Benyamini, A. J. Millis & D. M. Kennes. (2022) Anti-Poiseuille flow: Increased vortex velocity at superconductor edges. Physical Review B 105:22.
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Jishan Fan & Tohru Ozawa. (2021) Regularity Criteria for a Ginzburg-Landau-Navier-Stokes System. Funkcialaj Ekvacioj 64:3, pages 349-360.
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Hongjun Gao, Jishan Fan & Gen Nakamura. (2021) Weak-very weak uniqueness to the time-dependent Ginzburg–Landau model for superconductivity in . Results in Applied Mathematics 12, pages 100183.
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Soojung Kim & Xing-Bin Pan. (2021) Long time behavior and field-induced instabilities of smectic liquid crystals. Journal of Functional Analysis 281:3, pages 109036.
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Jishan Fan, Yuxi Hu & Gen Nakamura. (2021) Local well‐posedness for an isentropic compressible Ginzburg–Landau–Navier–Stokes with vacuum. Mathematische Nachrichten 294:5, pages 862-876.
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Erhan Coskun. (2021) On the properties of a single vortex solution of Ginzburg–Landau model of superconductivity. Physica A: Statistical Mechanics and its Applications 568, pages 125731.
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Zhidong Chen, Huadong Yong & Youhe Zhou. (2021) Manipulation of vortex arrays with thermal gradients by applying dynamic heat sources. Superconductor Science and Technology 34:4, pages 045005.
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Qiang Du, Lili Ju, Xiao Li & Zhonghua Qiao. (2021) Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes. SIAM Review 63:2, pages 317-359.
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Jishan Fan, Yasuhide Fukumoto & Yong Zhou. (2020) Regularity criteria for a Ginzburg‐Landau‐Navier‐Stokes in superfluidity in Rn. Mathematical Methods in the Applied Sciences 43:10, pages 6542-6552.
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Zhidong Chen, Huadong Yong & Youhe Zhou. (2020) The heat dissipations and vortices motion in the open superconducting square tube. Physica C: Superconductivity and its Applications 574, pages 1353659.
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Jishan Fan, Lulu Jing, Gen Nakamura & Tong Tang. (2019) A Note on a Non-isothermal Model for Superconductivity. Bulletin of the Malaysian Mathematical Sciences Society 43:4, pages 3027-3034.
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Jishan Fan & Yong Zhou. (2020) A note on the time-dependent Ginzburg–Landau model for superconductivity in . Applied Mathematics Letters 103, pages 106208.
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Jishan Fan & Yong Zhou. (2020) A regularity criterion to the time-dependent Ginzburg-Landau model for superconductivity in . Journal of Mathematical Analysis and Applications 483:2, pages 123653.
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Jishan Fan &  Yong Zhou. (2020) Existence and uniqueness for a Ginzburg-Landau system for superconductivity. Electronic Journal of Differential Equations 2020:01-132.
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Jishan Fan, Zhaoyun Zhang & Yong Zhou. (2019) Regularity Criteria for a Ginzburg–Landau–Navier–Stokes in a Bounded Domain. Bulletin of the Malaysian Mathematical Sciences Society 43:1, pages 1009-1024.
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Jishan Fan & Tohru Ozawa. (2018) Global Well-posedness of Weak Solutions to the Time-dependent Ginzburg-Landau Model for Superconductivity. Taiwanese Journal of Mathematics 22:4.
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Jishan Fan, Bessem Samet & Yong Zhou. (2018) Uniform regularity for a 3D time-dependent Ginzburg–Landau model in superconductivity. Computers & Mathematics with Applications 75:9, pages 3244-3248.
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Gautam Iyer & Daniel Spirn. (2017) A Model for Vortex Nucleation in the Ginzburg–Landau Equations. Journal of Nonlinear Science 27:6, pages 1933-1956.
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Hyungjin Huh. (2017) Global solutions to time-dependent Ginzburg–Landau–Chern–Simons equations. Journal of Mathematical Analysis and Applications 455:1, pages 714-726.
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Buyang Li & Chaoxia Yang. (2017) Global well-posedness of the time-dependent Ginzburg–Landau superconductivity model in curved polyhedra. Journal of Mathematical Analysis and Applications 451:1, pages 102-116.
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Min Xiao, Jishan Fan & Guoxi Ni. (2016) Weak solutions to the Ginzburg–Landau model in superconductivity with the Coulomb gauge. Mathematical Methods in the Applied Sciences 40:8, pages 2872-2877.
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Jishan Fan & Tohru Ozawa. 2017. New Trends in Analysis and Interdisciplinary Applications. New Trends in Analysis and Interdisciplinary Applications 301 306 .
J. Barba-Ortega, H.M. Carrillo & C.A. Sjogreen-Blanco. (2016) Unidimensional thermal gradients Tn in a nanoscopic superconductor. Physica C: Superconductivity and its Applications 525-526, pages 61-64.
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Zeling Ma, Xingzhe Wang & Youhe Zhou. (2016) Vortex and characteristics of prestrained type-II deformable superconductors under magnetic fields. Physica C: Superconductivity and its Applications 523, pages 10-18.
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Buyang Li & Zhimin Zhang. (2015) A new approach for numerical simulation of the time-dependent Ginzburg–Landau equations. Journal of Computational Physics 303, pages 238-250.
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Huadong Gao & Weiwei Sun. (2015) An efficient fully linearized semi-implicit Galerkin-mixed FEM for the dynamical Ginzburg–Landau equations of superconductivity. Journal of Computational Physics 294, pages 329-345.
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Jishan Fan, Hongjun Gao & Boling Guo. (2015) Uniqueness of Weak Solutions to the 3D Ginzburg–Landau Superconductivity Model. International Mathematics Research Notices 2015:5, pages 1239-1246.
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Jishan Fan & Tohru Ozawa. (2013) Global existence of strong solutions to a time‐dependent 3D Ginzburg‐Landau model for superconductivity with partial viscous terms. Mathematische Nachrichten 286:17-18, pages 1792-1796.
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Jishan Fan & Guoxi Ni. (2013) Uniform existence for a 3D time-dependent Ginzburg–Landau model in superconductivity. Applied Mathematics Letters 26:8, pages 814-819.
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Mariusz Gil & Stanisław Wędrychowicz. (2013) Schauder-Tychonoff Fixed-Point Theorem in Theory of Superconductivity. Journal of Function Spaces and Applications 2013, pages 1-12.
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Jishan Fan & Tohru Ozawa. (2011) Uniqueness of weak solutions to the Ginzburg-Landau model for superconductivity. Zeitschrift für angewandte Mathematik und Physik 63:3, pages 453-459.
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Yanzhi Zhang, Janet Peterson & Max Gunzburger. (2011) Maximizing critical currents in superconductors by optimization of normal inclusion properties. Physica D: Nonlinear Phenomena 240:21, pages 1701-1713.
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Tingchun Wang & Boling Guo. (2011) Analysis of some finite difference schemes for two-dimensional Ginzburg-Landau equation. Numerical Methods for Partial Differential Equations 27:5, pages 1340-1363.
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Alessia Berti, Valeria Berti & Ivana Bochicchio. (2011) Global and exponential attractors for a Ginzburg-Landau model of superfluidity. Discrete & Continuous Dynamical Systems - S 4:2, pages 247-271.
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Ian Tice. (2010) Ginzburg‐Landau vortex dynamics driven by an applied boundary current. Communications on Pure and Applied Mathematics 63:12, pages 1622-1676.
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Qiang Du, Juncheng Wei & Chunyi Zhao. (2010) Vortex Solutions of the High-$\kappa$ High-Field Ginzburg–Landau Model with an Applied Current. SIAM Journal on Mathematical Analysis 42:6, pages 2368-2401.
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Maurizio Grasselli, Hao Wu & Songmu Zheng. (2009) Convergence to Equilibrium for Parabolic-Hyperbolic Time-Dependent Ginzburg–Landau–Maxwell Equations. SIAM Journal on Mathematical Analysis 40:5, pages 2007-2033.
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Jishan Fan & Hongjun Gao. (2007) Uniqueness of weak solutions of time-dependent 3-D Ginzburg-Landau model for superconductivity. Frontiers of Mathematics in China 2:2, pages 183-189.
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Valeria Berti & Mauro Fabrizio. (2007) Existence and uniqueness for a non-isothermal dynamical Ginzburg–Landau model of superconductivity. Mathematical and Computer Modelling 45:9-10, pages 1081-1095.
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Daniel Spirn. (2003) Vortex Motion Law for the Schrödinger--Ginzburg--Landau Equations. SIAM Journal on Mathematical Analysis 34:6, pages 1435-1476.
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