Ergodicity for SPDEs driven by divergence-free transport noise

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.

💡 Research Summary

The paper investigates the long‑time behavior of a class of McKean–Vlasov stochastic partial differential equations (SPDEs) on the $d$‑dimensional torus, driven by a common, divergence‑free transport noise that is white in time and colored in space. The deterministic part of the equation, \