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

TL;DR

This paper proves the global existence of weak solutions for a Landau-Lifshitz equation with helical derivatives, using specialized Sobolev spaces and energy estimates for chiral boundary conditions.

Contribution

It introduces Sobolev spaces tailored to helical derivatives and establishes energy estimates to demonstrate global weak solutions for the chiral Landau-Lifshitz problem.

Findings

Proved global existence of weak solutions with chiral boundary conditions.

Developed Sobolev spaces adapted to helical derivatives.

Established energy estimates compatible with boundary conditions.

Abstract

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.