Existence, uniqueness and regularity of solutions to the stochastic Landau-Lifschitz-Slonczewski equation

TL;DR

This paper establishes the existence, uniqueness, and regularity of solutions for a stochastic Landau-Lifschitz-Slonczewski equation modeling magnetization in nanowires under spin torque with gradient noise.

Contribution

It provides the first rigorous proof of well-posedness and regularity for the stochastic LLS equation with multiplicative gradient noise.

Findings

Proved existence of pathwise solutions.

Established uniqueness of solutions.

Demonstrated regularity properties of solutions.

Abstract

In this paper we are concerned with the stochastic Landau-Lifshitz-Slonczewski equation (LLS) that describes magnetisation of an inifnite nanowire evolving under current driven spin torque. The current brings into the system a multiplicative gradient noise that appears as a transport term in the equation. We prove the existence, uniqueness and regularity of pathwise solutions to this equation.