Landau-Lifshitz-Slonczewski equations: Global weak and classical solutions

Christof Melcher*, Mariya Ptashnyk

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


We consider magnetization dynamics under the influence of a spin-polarized current, given in terms of a spin-velocity field v, governed by the following modification of the Landau- Lifshitz-Gilbert equation {equation presented} called the Landau- Lifshitz-Slonczewski equation. We focus on the situation of magnetizations defined on the entire Euclidean space m(t): R3 → S2. Our construction of global weak solutions relies on a discrete lattice approximation in the spirit of Slonczevski's spin-transfer-torque model and provides a rigorous justification of the continuous model. Using the method of moving frames, we show global existence and uniqueness of classical solutions under smallness conditions on the initial data in terms of the W1,3 norm and on the spin velocity v in terms of weighted-in-time Lebesgue norms, both optimal with respect to the natural scaling of the equation.

Original languageEnglish
Pages (from-to)407-429
Number of pages23
JournalSIAM Journal on Mathematical Analysis
Issue number1
Publication statusPublished - 2013


  • Continuum limit of lattice approximations
  • Landau-Lifshitz-Gilbert equations
  • Moving-frame method
  • Spin-transfer torque

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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