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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.04107 |
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| _version_ | 1866915257783418880 |
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| author | Goldys, Ben Jiao, Chunxi Melcher, Christof |
| author_facet | Goldys, Ben Jiao, Chunxi Melcher, Christof |
| contents | 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{à}dl{à}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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04107 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pathwise Solvability and Bubbling in 2D Stochastic Landau-Lifshitz-Gilbert Equations Goldys, Ben Jiao, Chunxi Melcher, Christof Analysis of PDEs Probability 60H15, 35A02, 35A21, 35K59, 35Q60 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{à}dl{à}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. |
| title | Pathwise Solvability and Bubbling in 2D Stochastic Landau-Lifshitz-Gilbert Equations |
| topic | Analysis of PDEs Probability 60H15, 35A02, 35A21, 35K59, 35Q60 |
| url | https://arxiv.org/abs/2504.04107 |