Pathwise Solvability and Bubbling in 2D Stochastic Landau-Lifshitz-Gilbert Equations
Analysis of PDEs
2025-04-28 v2 Probability
Abstract
We investigate the stochastic Landau-Lifshitz-Gilbert (LLG) equation on a periodic 2D domain, driven by infinite-dimensional Gaussian noise in a Sobolev class. We establish strong local well-posedness in the energy space and characterize blow-up at random times in terms of energy concentration at small scales (bubbling). By iteration, we construct pathwise global weak solutions, with energy evolving as a c{\`a}dl{\`a}g process, and prove uniqueness within this class. These results offer a stochastic counterpart to the deterministic concept of Struwe solutions. The approach relies on a transformation that leads to a magnetic Landau-Lifshitz-Gilbert equation with random gauge coefficients.
Keywords
Cite
@article{arxiv.2504.04107,
title = {Pathwise Solvability and Bubbling in 2D Stochastic Landau-Lifshitz-Gilbert Equations},
author = {Ben Goldys and Chunxi Jiao and Christof Melcher},
journal= {arXiv preprint arXiv:2504.04107},
year = {2025}
}