Continuity equation in LlogL for the 2D Euler equations under the enstrophy measure

TL;DR

This paper establishes the existence of solutions to the continuity equation in Hilbert spaces for the 2D Euler equations with random initial conditions, focusing on LlogL densities relative to the enstrophy measure.

Contribution

It proves the existence of solutions in a general setting for the continuity equation associated with the 2D Euler equations under the enstrophy measure.

Findings

Existence of solutions in Hilbert spaces for the continuity equation.

Solutions are valid for LlogL densities with respect to the enstrophy measure.

Extends previous work on the 2D Euler equations with random initial conditions.

Abstract

The 2D Euler equations with random initial condition has been investigates by S. Albeverio and A.-B. Cruzeiro in [1] and other authors. Here we prove existence of solutions for the associated continuity equation in Hilbert spaces, in a quite general class with LlogL densities with respect to the enstrophy measure.