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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.

MSC:

35Q35 PDEs in connection with fluid mechanics
35K51 Initial-boundary value problems for second-order parabolic systems
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