Stochastic homogenization with space-time ergodic divergence-free drift
Probability
2022-08-01 v1 Analysis of PDEs
Abstract
We prove that diffusion equations with a space-time stationary and ergodic, divergence-free drift homogenize in law to a deterministic stochastic partial differential equation with Stratonovich transport noise. In the absence of spatial ergodicity, the drift is only partially absorbed into the skew-symmetric part of the flux through the use of an appropriately defined stream matrix. This leaves a time-dependent, spatially-homogenous transport which, for mildly decorrelating fields, converges to a Brownian noise with deterministic covariance in the homogenization limit. The results apply to uniformly elliptic, stationary and ergodic environments in which the drift admits a suitably defined stationary and -integrable stream matrix.
Cite
@article{arxiv.2207.14555,
title = {Stochastic homogenization with space-time ergodic divergence-free drift},
author = {Benjamin Fehrman},
journal= {arXiv preprint arXiv:2207.14555},
year = {2022}
}