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Cauchy problem for the time-dependent Ginzburg–Landau model of superconductivity

Published online by Cambridge University Press:  11 July 2007

A. Rodriguez-Bernal  and
B. Wang
A. Rodriguez-Bernal
Affiliation:
Departamento de Matematica Aplicada, Universidad Complutense de Madrid, Madrid 28040, Spain
B. Wang
Affiliation:
Department of Applied Mathematics, Tsinghua University, Beijing 100084, People's Republic of China
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Abstract

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The Cauchy problem for the time-dependent Ginzburg–Landau equations of superconductivity in Rd (d = 2, 3) is investigated in this paper. When d = 2, we show that the Cauchy problem for this model is well posed in L2. When d = 3, we establish the existence result of solutions for L3 initial data and the uniqueness result for L4 initial data.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 6 , December 2000 , pp. 1383 - 1404
Copyright
Copyright © Royal Society of Edinburgh 2000