Hausdorff dimension of the level sets of some stochastic PDEs from fluid dynamics

TL;DR

This paper investigates the Hausdorff dimension of level sets in certain stochastic fluid dynamics models, specifically Navier-Stokes -models, under random forcing, providing probabilistic dimension estimates.

Contribution

It establishes the Hausdorff dimension of level sets for Navier-Stokes -models with Gaussian white noise forcing, a novel probabilistic analysis in stochastic fluid dynamics.

Findings

Hausdorff dimension of level sets determined with positive probability

Results apply to Navier-Stokes -models at finite viscosity

Analysis involves stochastic PDEs with rough Gaussian noise

Abstract

We determine with positive probability the Hausdorff dimension of the level sets of a class of Navier-Stokes \alpha-models at finite viscosity, forced by mildly rough Gaussian white noise.