# Exact Solutions for the Fluid Impulse for Incompressible and Compressible Flows

## TL;DR

This paper constructs exact solutions for the fluid impulse density in both incompressible and compressible barotropic flows, extending previous impulse formulations and discussing their physical significance.

## Contribution

It introduces exact solutions for fluid impulse density applicable to incompressible and compressible barotropic flows, expanding the theoretical framework.

## Key findings

- Exact solutions for fluid impulse density are derived.
- The physical significance of these solutions is discussed.
- The work extends impulse formulations to compressible flows.

## Abstract

Impulse formulations of the Euler (and Navier-Stokes) equations were considered by Kuz'min [1] and Oseledets [2] and different impulse formulations are produced by various gauge transformations (Russo and Smereka[3]). The extension of the Kuz'min-Oseledets formulation to the compressible, barotropic case was considered by Tur and Yanovsky [4] and Shivamoggi [5]. Here, we construct exact solutions for the fluid impulse density for incompressible and compressible barotropic flows and discuss their physical signifcance.