Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (3): 729-739.

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

Penghong Zhong,Xingfa Chen*()   

  1. Department of Mathematics, Guangdong University of Education, Guangzhou 510303
  • Received:2020-02-21 Online:2021-06-26 Published:2021-06-09
  • Contact: Xingfa Chen
  • Supported by:
    NSF for Young Scientists of China(11601092);the Project for Young Creative Talents of Ordinary University of Guangdong Province(2014KQNCX228);the PhD Start-up Fund of NSF of Guangdong Province(2014A030310330);the Special Innovation Projects of Universities in Guangdong Province(2018KTSCX161);the Funds of Guangzhou Science and Technology(201607010352)


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