# Limiting behavior of scaled general Euler equations of compressible fluid flow

## TL;DR

This paper investigates the limiting behavior of solutions to scaled generalized Euler equations for compressible fluids, showing convergence to a model for large-scale universe structure formation, with entropy admissibility established.

## Contribution

It demonstrates the convergence of solutions of scaled Euler equations to a non-hyperbolic model in the large-scale limit, including explicit entropy pair construction.

## Key findings

- Solutions include shock and rarefaction waves
- Distributional limits converge to a cosmological model
- Constructed explicit entropy and flux pairs

## Abstract

The aim of this article is to study the limiting behavior of the solutions for the scaled generalized Euler equations of compressible fluid flow. When the initial data is of Riemann type, we showed the existence of solution which consists of shock waves and rarefaction waves and that the distributional limit of the solutions for this system converges to the solution of a non-strictly hyperbolic system, called one dimensional model for large scale structure formation of universe as the scaling parameter vanishes. An explicit entropy and entropy flux pair are also constructed for the particular flux function (Brio system) and it is shown that the solution constructed is entropy admissible. This is a continuation of our work[23].