A remark on the regularity for the landau-lifshitz equation

Abstract

We consider the initial value problem of the Landau-Lifshitz equation in the pure isotropic case and without external magnetic fields. It is proved that in two space dimensional cases any weak solution with finite energy is unique and is smooth with the exception of at most finitely many points.

Keywords:

• Nonlinear Parabolic equation
• Uniqueness
• Regularity
• Hodge decomposition
• Landau-Lifshitz equation