Global regular solutions for Landau-Lifshitz equation

Abstract

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 L²(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 L²(0, T; L^∞) can be cancelled.