Ergodicity for SPDEs driven by divergence-free transport noise
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917232888512512 |
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| author | Gess, Benjamin Gvalani, Rishabh S. Martini, Adrian |
| author_facet | Gess, Benjamin Gvalani, Rishabh S. Martini, Adrian |
| contents | We study the ergodic behaviour of the McKean-Vlasov equations driven by common, divergence-free transport noise. In particular, we show that in dimension $d\geq 2$, if the noise is mixing and sufficiently strong it can enforce the uniqueness of invariant probability measures, even if the deterministic part of equation has multiple steady states. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_22056 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ergodicity for SPDEs driven by divergence-free transport noise Gess, Benjamin Gvalani, Rishabh S. Martini, Adrian Probability Analysis of PDEs Dynamical Systems 37A25 (Primary) 37H15, 35R60, 60H15, 76F25 (Secondary) We study the ergodic behaviour of the McKean-Vlasov equations driven by common, divergence-free transport noise. In particular, we show that in dimension $d\geq 2$, if the noise is mixing and sufficiently strong it can enforce the uniqueness of invariant probability measures, even if the deterministic part of equation has multiple steady states. |
| title | Ergodicity for SPDEs driven by divergence-free transport noise |
| topic | Probability Analysis of PDEs Dynamical Systems 37A25 (Primary) 37H15, 35R60, 60H15, 76F25 (Secondary) |
| url | https://arxiv.org/abs/2601.22056 |