Ergodicity for SPDEs driven by divergence-free transport noise

• Authors: Benjamin Gess, Rishabh S. Gvalani, Adrian Martini
• Preprint year: 2026
• First public date: 2026-01-29
• arXiv: 2601.22056

Abstract

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.

Associated SAiS members

• Benjamin Gess
• Adrian Martini

Associated projects

• FluCo

Research areas

• SPDEs
• Stochastic Dynamics
• Stochastic Fluid Dynamics
• Sampling

BibTeX

@article{arxiv260122056,
  title = {Ergodicity for SPDEs driven by divergence-free transport noise},
  author = {Benjamin Gess and Rishabh S. Gvalani and Adrian Martini},
  year = {2026},
  eprint = {2601.22056},
  archivePrefix = {arXiv},
  primaryClass = {math.PR}
}