Random Splitting of Fluid Models: Unique Ergodicity and Convergence

We introduce a family of stochastic models motivated by the study nonequilibrium steady states fluid equations. These decompose deterministic dynamics interest into fundamental building blocks, i.e., minimal vector fields preserving some aspects original dynamics. Randomness is injected sequentially following each field for random amount time. show under general assumptions that these possess unique invariant measure and converge almost surely to original, model in small noise limit. apply our construction Lorenz-96 equations, often used studies chaos data assimilation, Galerkin approximations 2D Euler Navier-Stokes An interesting feature developed they directly conservative not just those with excitation dissipation.