# A new additive decomposition of velocity gradient

## TL;DR

This paper introduces a novel additive decomposition of the velocity gradient tensor to overcome limitations of the classical Cauchy-Stokes decomposition, emphasizing a rotation tensor expressed as an exponential of a skew-symmetric matrix.

## Contribution

It proposes a new additive decomposition of the velocity gradient that explicitly incorporates a rotation tensor as an exponential map, improving upon existing methods.

## Key findings

- Provides a mathematically consistent additive decomposition
- Eliminates the infinitesimal rotation limitation
- Enhances understanding of velocity gradient structure

## Abstract

To avoid the infinitesimal rotation nature of the Cauchy-Stokes decomposition of velocity gradient, the letter proposes an new additive decomposition in which one part is a SO(3) rotation tensor $Q=\exp W$.