(untitled) (Journal of Partial Differential Equations, 2020)
In this paper, we consider the Cauchy problem for two dimensional Landau-Lifshitz equation on 2-dimenslonal Riemannian manifold M without boundary. We proved that if u: M × R_+ → S², is a weak solution, then u is unique and smooth on M × R_+ with the exception of finitely many points.