Statistical instability of a stochastically forced shear

For a fixed elongated rectangular torus and forcing in the single vorticity mode sin y, the stochastically forced two-dimensional Navier–Stokes equations have, at sufficiently small viscosity, an ergodic invariant measure not supported on shear flows. This release archives the project website, which contains a digested account of the argument and the full raw proof. The raw proof was written by an AI model and has not been checked by a human. Project website: https://transverse-instability.github.io/. The project is listed on mathStoa, an archive for open mathematical research projects: https://math-stoa.org/.