Hyperviscous stochastic Navier-Stokes equations with white noise invariant measure in two dimensions

TL;DR

This paper establishes the existence and uniqueness of solutions for a hyperviscous stochastic Navier-Stokes equation in two dimensions, with initial conditions linked to the Gibbs measure, in both torus and whole space settings.

Contribution

It proves well-posedness of a hyperviscous stochastic Navier-Stokes model with Gibbs measure initial conditions in 2D, extending previous results to new settings.

Findings

Existence of martingale solutions in 2D hyperviscous stochastic Navier-Stokes

Uniqueness of solutions under Gibbs measure initial conditions

Results applicable in both torus and whole space domains

Abstract

We prove existence and uniqueness of martingale solutions to a (slightly) hyperviscous stochastic Navier-Stokes equation in 2d with initial conditions absolutely continuous with respect to the Gibbs measure associated to the energy, getting the results both in the torus and in the whole space setting.