Kolmogorov equations associated to the stochastic 2D Euler equations

TL;DR

This paper investigates the Kolmogorov equation linked to stochastic 2D Euler equations with transport noise, using Fourier, Galerkin, and Wiener chaos methods to analyze the impact of noise regularity.

Contribution

It introduces a direct analytical approach that generalizes previous results and clarifies how noise roughness affects the solutions of the Kolmogorov equation.

Findings

Generalized existing results on stochastic 2D Euler equations

Analyzed the influence of noise regularity on solutions

Developed a method combining Fourier, Galerkin, and Wiener chaos techniques

Abstract

The Kolmogorov equation associated to a stochastic 2D Euler equations with transport type noise and random initial conditions is studied by a direct approach, based on Fourier analysis, Galerkin approximation and Wiener chaos methods. The method allows us to generalize previous results and to understand the role of the regularity of the noise, in relation to a limiting value of roughness.