Special Session 11: Stochastic Partial Differential Equations

Ergodicity for SPDEs driven by divergence-free transport noise
Adrian Martini
Technical University of Berlin
Germany
Co-Author(s):    Benjamin Gess, Rishabh S. Gvalani
Abstract:
We study the ergodic behaviour of McKean--Vlasov equations driven by common, divergence-free transport noise. In particular, we show that in dimensions greater or equal to 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. This is joint work with Benjamin Gess and Rishabh S. Gvalani.