Abstract
In this paper, we describe several stationary conditions on weak solutions to the inhomogeneous Landau-Lifshitz equation, which ensure the partial regularity. For certain class of proper stationary weak solutions, a compactness result of the solutions, a finite Hausdorff measure result of the t-slice energy concentration sets and an asymptotic limit result of the Radon measures are proved. We also present a subtle rectifiability result for the energy concentration set of certain sequence of strong stationary weak solutions.
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Project supported by the National Natural Science Foundation of China (No. 10571158) and the Natural Science Foundation of Zhejiang Province, China (No. Y605076)
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Fang, Dy., Li, Tl. & Xue, Ry. Some stationary weak solutions to inhomogeneous Landau-Lifshitz equations in three dimensions. J. Zhejiang Univ. - Sci. A 8, 949–956 (2007). https://doi.org/10.1631/jzus.2007.A0949
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DOI: https://doi.org/10.1631/jzus.2007.A0949