We establish existence of partially regular weak solutions for the Landau-Lifshitz equation in three space dimensions for smooth initial data of finite Dirichlet energy. We show that the singular set of such a solution has locally finite 3-dimensional parabolic Hausdorff measure. The construction relies on an approximation based on the Ginzburg-Landau energy.
Institute for Mathematics and Its Applications>IMA Preprints Series
Existence of partially regular solutions for Landau-Lifshitz equations in R3.
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