J. Austral. Math. Soc.  72 (2002), 299-316

Landau-Lifshitz equation of ferromagnetism with external magnetic field

P. Y. H. Pang   Department of Mathematics   National University of Singapore   2 Science Drive 2   Republic of Singapore 117543   matpyh@nus.edu.sg J. Xiao   Department of Mathematics   National University of Singapore   2 Science Drive 2   Republic of Singapore 117543   Current address:   Department of Mathematics   University of Minnesota   Minneapolis MN 55455   USA   xiao@math.umn.edu and F. Zhou   Department of Mathematics   East China Normal University   Shanghai 200062   People's Republic of China   fzhou@math.ecnu.edu.cn

Abstract

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.

Download the article in PDF format (size 151 Kb)

TeXAdel Scientific Publishing ©  Australian MS