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Global weak solutions to Landau-Lifshtiz systems with spin-polarized transport

  • * Corresponding author: Youde Wang

    * Corresponding author: Youde Wang

The authors are supported by NSFC grant No.11731001

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  • In this paper, we consider the Landau-Lifshitz-Gilbert systems with spin-polarized transport from a bounded domain in $ \mathbb{R}^3 $ into $ S^2 $ and show the existence of global weak solutions to the Cauchy problems of such Landau-Lifshtiz systems. In particular, we show that the Cauchy problem to Landau-Lifshitz equation without damping but with diffusion process of the spin accumulation admits a global weak solution. The Landau-Lifshtiz system with spin-polarized transport into a compact Lie algebra is also discussed and some similar results are proved. The key ingredients of this article consist of the choices of test functions and approximate equations.

    Mathematics Subject Classification: 35D30, 35G20, 35G25.


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