# Entropy in Exact 2D Navier–Stokes and 3D Burgers Gas Flows

## TL;DR

The paper presents two exact solutions for gas dynamics in 2D and 3D, including entropy production calculations.

## Contribution

The novelty lies in constructing explicit exact solutions for Navier–Stokes and Burgers’ equations with entropy production analysis.

## Key findings

- A steady vortex solution is derived for 2D Navier–Stokes with entropy production expressions.
- A time-dependent radial solution for 3D Burgers’ equation is presented with shock-like behavior at low Reynolds numbers.

## Abstract

Two exact solutions are constructed for viscous compressible gas dynamics in two and three dimensions. The first is a steady vortex, with explicit solutions for the full Navier–Stokes system of velocity, density, temperature and pressure. In contrast, the second is a time-dependent radial solution to the 3D vector Burgers’ equation, with a constant injection rate from a spherical interior surface. That solution is shock-like at low Reynolds numbers. In both cases, expressions are given for the local density of entropy production.