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arXiv · 2601.22056

Ergodicity for SPDEs driven by divergence-free transport noise

Benjamin Gess·Rishabh S. Gvalani·Adrian Martini
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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.

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Benjamin Gess, Rishabh S. Gvalani, Adrian Martini. 2026-01-29. Ergodicity for SPDEs driven by divergence-free transport noise. https://arxiv.org/abs/2601.22056

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