Large-scale regularity in stochastic homogenization with divergence-free drift
Benjamin Fehrman · The Annals of Applied Probability · 2023
We provide a proof of stochastic homogenization for random environments with a mean zero, divergence-free drift. We prove that the environment homogenizes weakly in H1 if the drift admits a stationary L2-integrable stream matrix, and we prove that the two-scale expansion converges strongly in H1 if the drift admits a stationary Ld∨(2+δ)-integrable stream matrix. Additionally, under this stronger integrability assumption, we show that the environment almost surely satisfies a large-scale Hölder regularity estimate and first-order Liouville principle.