Landau-Lifshitz-Bloch equation on Riemannian manifold
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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.
KeywordsOrientable vector bundle Riemannian curvature tensor on vector bundle Sobolev space on vector bundle
MSC35A01 35A02 35K10
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