English

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 L2L^2-integrable stream matrix.

Keywords

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}
}
R2 v1 2026-06-25T01:19:38.102Z