Existence of partially regular solutions for Landau-Lifshitz equations in R-3

摘要

We establish the existence of partially regular weak solutions for the Landau Lifshitz equation in three space dimensions for smooth initial data of finite Dirichlet energy. The construction is based on Ginzburg-Landau approximation. The new key ingredient is a nonlocal representation formula for the penalty term that permits us to take advantage of the special trilinear structure of the limiting nonlinearity.