# Optimal density lower bound on nonisentropic gas dynamics

## TL;DR

This paper establishes a time-dependent lower bound on the density of smooth nonisentropic compressible Euler flows, demonstrating it decreases at an optimal rate of O(1/(1+t)) over time.

## Contribution

It provides the first proven optimal lower bound on density decay for nonisentropic Euler equations in smooth flows.

## Key findings

- Density remains bounded below by a rate of O(1/(1+t)).
- The lower bound is proven to be optimal in order.
- Results apply to general smooth nonisentropic flows.

## Abstract

In this paper, we prove a time dependent lower bound on density in the optimal order $O(1/(1+t))$ for the general smooth nonisentropic flow of compressible Euler equations.