# Statistical solutions and Onsager's conjecture

## TL;DR

This paper proves a version of Onsager's conjecture for statistical solutions of the incompressible Euler equations, providing new insights into energy conservation and offering a novel proof for weak solutions.

## Contribution

It introduces a statistical solutions framework for Onsager's conjecture and establishes energy conservation results within this context, extending previous work on weak solutions.

## Key findings

- Proves Onsager's conjecture for statistical solutions.
- Provides a new proof for the conservative direction of Onsager's conjecture.
- Enhances understanding of energy conservation in fluid dynamics.

## Abstract

We prove a version of Onsager's conjecture on the conservation of energy for the incompressible Euler equations in the context of statistical solutions, as introduced recently by Fjordholm et al. As a byproduct, we also obtain a new proof for the conservative direction of Onsager's conjecture for weak solutions. Dedicated to Edriss S. Titi on the occasion of his 60th birthday.