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Global regular solutions for Landau-Lifshitz equation. (English) Zbl 1222.35150
Summary: In this note, we prove that there exists a unique global regular solution for multidimensional Landau-Lifshitz equation if the gradient of solutions can be bounded in space $L ^{2}(0, T; L ^{\infty })$. Moreover, for the two-dimensional radial symmetric Landau-Lifshitz equation with Neumann boundary condition in the exterior domain, this hypothesis in space $L ^{2}(0, T; L ^{\infty })$ can be cancelled.

35Q35PDEs in connection with fluid mechanics
35K51Second-order parabolic systems, initial bondary value problems
Full Text: DOI
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