Onsager's conjecture on the energy conservation for solutions of Euler equations in bounded domains

TL;DR

This paper proves the conservation of energy part of Onsager's conjecture for solutions of Euler equations in bounded domains, confirming that solutions with Hölder exponent greater than 1/3 conserve energy.

Contribution

It establishes the energy conservation aspect of Onsager's conjecture specifically for bounded domains, advancing understanding of Euler solutions.

Findings

Energy conservation holds for solutions with Hölder exponent > 1/3 in bounded domains.

The paper confirms the conservation part of Onsager's conjecture in this setting.

It provides mathematical proof for energy conservation in bounded Euler flows.

Abstract

The Onsager's conjecture has two parts: conservation of energy, if the exponent is larger than $1/3$ and the possibility of dissipative Euler solutions, if the exponent is less or equal than $1/3$. The paper proves half of the conjecture, the conservation part, in bounded domains.