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Global weak solutions for Landau-Lifshitz flows and heat flows associated to micromagnetic energy functional

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The authors are supported partially by NSFC grant (No.11731001). The author Y. Wang is supported partially by NSFC grant (No.11971400) and Guangdong Basic and Applied Basic Research Foundation Grant (No. 2020A1515011019)

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  • We follow the idea of Wang [21] to show the existence of global weak solutions to the Cauchy problems of Landau-Lifshtiz type equations and related heat flows from a $ n $-dimensional Euclidean domain $ \Omega $ or a $ n $-dimensional closed Riemannian manifold $ M $ into a 2-dimensional unit sphere $ \mathbb{S}^{2} $. Our conclusions extend a series of related results obtained in the previous literature.

    Mathematics Subject Classification: Primary: 35Q60, 78A25; Secondary: 58J35.

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