Landau-Lifshitz方程平面波解的全局光滑性

Abstract

Abstract:

In this paper, we study the n-dimensional plane wave solution of the Landau-Lifshtz equation on $\mathbb{S}^2$. Based on the Hasimoto transformation, the equivalent plane wave type Schrödinger equation is obtained. By the Strichartz estimation and energy method under Fourier transform, the global existence of this solution is proved under a small initial value. The global solution obtained here is smooth and the norm falls in any order Hilbert space. The results in this paper improve the regularity of the solution in the paper^[3].

Key words: Landau-Lifshitz equation, Existence, Smooth solution, Regularity

CLC Number:

O175.29

Penghong Zhong,Xingfa Chen. Global Smoothness of the Plane Wave Solutions for Landau-Lifshitz Equation[J].Acta mathematica scientia,Series A, 2021, 41(3): 729-739.

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References

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Global Smoothness of the Plane Wave Solutions for Landau-Lifshitz Equation

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