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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 ). 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 ) can be cancelled.
MSC:
35Q35PDEs in connection with fluid mechanics
35K51Second-order parabolic systems, initial bondary value problems
References:
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