# On the energy equality for solutions to Newtonian and non-Newtonian fluids

## TL;DR

This paper investigates the conditions under which weak solutions to both Newtonian and non-Newtonian incompressible fluids satisfy the energy equality, offering new insights and improvements over existing results.

## Contribution

It extends and refines energy equality conditions for non-Newtonian fluids, aligning them with or surpassing known Newtonian results, and provides a new interpretation of the Shinbrot condition.

## Key findings

- Improved energy equality conditions for non-Newtonian fluids
- Equivalent or better results than existing Newtonian fluid theories
- A novel interpretation of the Shinbrot condition

## Abstract

We are concerned with the energy equality for weak solutions to Newtonian and non-Newtonian incompressible fluids. In particular, the results obtained for non-Newtonian fluids, after restriction to the Newtonian case, equal or improve the known results. Furthermore, a new result below allows an interpretation of the classical Shinbrot condition, coherent to the more recent results in the literature.