Landau-Lifshitz-Bloch equation on Riemannian manifold

  • Zonglin JiaEmail author
  • Boling Guo
Research Article


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.


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


35A01 35A02 35K10 


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© 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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