Some observations regarding brackets and dissipation

TL;DR

This paper explores a novel bracket formulation for dissipative systems like Navier-Stokes, incorporating a symmetric component similar to a generalized Poisson bracket, to better understand dissipation mechanisms.

Contribution

Introduces a new bracket formulation with symmetric components for dissipative systems, applied specifically to Navier-Stokes equations.

Findings

Proposes a symmetric bracket structure for dissipative dynamics.

Applies the bracket formulation to Navier-Stokes equations.

Provides insights into dissipation through the bracket approach.

Abstract

Some ideas relating to a bracket formulation for dissipative systems are considered. The formulation involves a bracket that is analogous to a generalized Poisson bracket, but possesses a symmetric component. Such a bracket is presented for the Navier-Stokes equations.