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Zbl 1222.35150
Guo, Boling; Han, Yongqian
Global regular solutions for Landau-Lifshitz equation. (English)
[J] Front. Math. China 1, No. 4, 538-568 (2006). ISSN 1673-3452; ISSN 1673-3576/e

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.

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
35K51

Keywords: Landau-Lifshitz equation; global regular solution

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