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 sufficiently 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.
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Jia, Z., Guo, B. Landau-Lifshitz-Bloch equation on Riemannian manifold. Front. Math. China 14, 45–76 (2019). https://doi.org/10.1007/s11464-019-0745-0
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DOI: https://doi.org/10.1007/s11464-019-0745-0