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Landau-Lifshitz-Bloch equation on Riemannian manifold

  • Zonglin JiaEmail author
  • Boling Guo
Research Article
  • 2 Downloads

Abstract

We bring in Landau-Lifshitz-Bloch equation on m-dimensional closed Riemannian manifold and prove that it admits a unique local solution. When m ⩾ 3 and the initial data in L-norm is suffciently small, the solution can be extended globally. Moreover, for m = 2, we can prove that the unique solution is global without assuming small initial data.

Keywords

Orientable vector bundle Riemannian curvature tensor on vector bundle Sobolev space on vector bundle 

MSC

35A01 35A02 35K10 

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Applied Physics and Computational MathematicsChina Academy of Engineering PhysicsBeijingChina

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