Existence of arbitrarily smooth solutions of the LLG equation in 3D with natural boundary conditions

TL;DR

This paper proves that the 3D Landau-Lifshitz-Gilbert equation with natural boundary conditions has arbitrarily smooth solutions near constant initial data, advancing understanding of its regularity properties.

Contribution

It establishes the existence of arbitrarily smooth solutions for the 3D LLG equation under natural boundary conditions close to constant initial states.

Findings

Existence of smooth solutions near constant initial data

Solutions are arbitrarily smooth in three dimensions

Results apply to the Landau-Lifshitz-Gilbert equation with Neumann boundary conditions

Abstract

We prove that the Landau-Lifshitz-Gilbert equation in three space dimensions with homogeneous Neumann boundary conditions admits arbitrarily smooth solutions, given that the initial data is sufficiently close to a constant function.