Global existence of weak solutions for Landau-Lifshitz equation with helical derivatives

In this paper, we investigate the chiral boundary value problem for the Landau-Lifshitz equation with helical derivatives. By introducing Sobolev spaces adapted to the helical derivative and establishing energy estimates that are compatible with the chiral boundary condition, we prove the global existence of weak solutions to this problem, both in the presence and in the absence of damping terms.