# Strong solvability of regularized stochastic Landau-Lifshitz-Gilbert equation

## TL;DR

This paper proves the strong solvability of a regularized stochastic Landau-Lifshitz-Gilbert equation, which is relevant for advanced micromagnetic models involving nanoscale topological solitons, ensuring topology preservation of initial data.

## Contribution

It demonstrates the existence of strong solutions for a regularized stochastic LLG equation, contrasting with the classical case, and highlights topology preservation.

## Key findings

- Regularized stochastic LLG equation is solvable in the strong sense.
- Topology of initial data is preserved almost surely.
- Regularization involves second-order derivatives in the energy functional.

## Abstract

We examine a stochastic Landau-Lifshitz-Gilbert equation based on an exchange energy functional containing second-order derivatives of the unknown field. Such regularizations are featured in advanced micromagnetic models recently introduced in connection with nanoscale topological solitons. We show that, in contrast to the classical stochastic Landau-Lifshitz-Gilbert equation based on the Dirichlet energy alone, the regularized equation is solvable in the stochastically strong sense. As a consequence it preserves the topology of the initial data, almost surely.