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We investigate the general Oseen--Frank energy for the Landau--Lifshitz equation of the ferromagnetic spin chain from $Bbb R^2$ to the unit sphere $S^2$. Our main results are global existence and uniqueness of weak solutions for large energy initial data. Moreover, the number of singular points for weak solutions is proved to be finite.

The Landau--Lifshitz Equation of the Ferromagnetic Spin Chain and Oseen--Frank Flow