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Global existence of weak solutions of a time-dependent 3-D Ginzburg-Landau model for superconductivity

โœ Scribed by Jishang Fan; Song Jiang

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
282 KB
Volume
16
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

Communicated by J. R. Ockendon Abstract--We study an initial boundary value problem for a time-dependent 3-D Ginzburg-Landau model of superconductivity. We prove the existence of global weak solutions with L 2 initial data and, hence, solve an open problem mentioned in [1]. (~) 2003 Elsevier Science Ltd. All rights reserved.

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The time-dependent Ginzburg-Landau equations of superconductivity in three spatial dimensions axe investigated in this paper. We establish the existence of global weak solutions for this model with any L p (p \_> 3) initial data. This work generalizes the results in . (~) 1999 Elsevier Science Ltd.

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## Abstract We prove the uniqueness of weak solutions of the 3โ€D timeโ€dependent Ginzburgโ€Landau equations for superโ€conductivity with initial data (__ฯˆ__~0~, __A__~0~)โˆˆ __L__^2^ under the hypothesis that (__ฯˆ__, __A__) โˆˆ __L__^__s__^(0, __T__; __L__^__r__,โˆž^) ร—$ L^{\bar s} $(0, __T__;$ L^{\bar r,