Global Weak Solutions to the Landau-Lifshitz System in 3D

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Abstract

By considering a general form of the Landau-Lifshitz equation under the influence of a homogeneous external magnetic fields, we prove that for a ferromagnetic body which occupies a bounded domain â„¦ in â„3 there exists a global weak solution either for the Dirichlet problem or for the Neumann problem. Although there is, in general, non-uniqueness result for the Landau-Lifshitz equation, the uniqueness result for the dynamic equation with constant initial data, which connects with the ground state of the magnetization in physical meanings, is pointed out. 

Keywords

Landau-lifshitz Equation , global solution , uniqueness , ground state
  • Daoyuan Fang Department of Mathematics, Zhejiang University, Hangzhou 310027, China.
  • Tailong Li Department of Mathematics, Zhejiang University, Hangzhou 310027, China.
  • Pages: 1-21
  • Date Published: 2006-08-01
  • Vol. 8 No. 2 (2006): CUBO, A Mathematical Journal

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Published

2006-08-01

How to Cite

[1]
D. Fang and T. Li, “Global Weak Solutions to the Landau-Lifshitz System in 3D”, CUBO, vol. 8, no. 2, pp. 1–21, Aug. 2006.

Issue

Vol. 8 No. 2 (2006): CUBO, A Mathematical Journal

Section

Articles