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Landau-Lifshitz equation of ferromagnetism with external magnetic field

Part of: Equations of mathematical physics and other areas of application Partial differential equations Applications to specific types of physical systems

Published online by Cambridge University Press:  09 April 2009

P. Y. H. Pang ,
J. Xiao  and
F. Zhou
P. Y. H. Pang
Affiliation:
Department of Mathematics, National University of singapore, 2 Science Drive 2, Republic of Singapore 117543 e-mail: matpyh@nus.edu.sg
J. Xiao
Affiliation:
Department of Mathematics, National University of singapore, 2 Science Drive 2, Republic of Singapore 117543
F. Zhou
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200062, People's Republic of China, e-mail: fzhou@math.ecnu.edu.cn
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Abstract

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In this article, we prove the existence and uniqueness of solution for the Cauchy problem of the Landau-Lifshitz equation of ferromagnetism with external magnetic field. We also show that the solution is globally regular with the exception of at most finitely many blow-up points. An energy identity at blow-up points is presented.

Keywords

Landau-Lifshitz equationregularityenergy identity

MSC classification

Secondary: 35Q60: PDEs in connection with optics and electromagnetic theory 35B65: Smoothness and regularity of solutions 82D40: Magnetic materials
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 3 , June 2002 , pp. 299 - 316
Copyright
Copyright © Australian Mathematical Society 2002

References

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