Limiting behavior of solutions for Euler equations of compressible fluid flow

TL;DR

This paper investigates how solutions to one-dimensional compressible Euler equations behave as pressure effects diminish, showing convergence to a limiting solution relevant for cosmological large-scale structure formation.

Contribution

It demonstrates the convergence of Euler solutions to a limit as pressure vanishes and compares different approximation methods for cosmological modeling.

Findings

Solutions converge in the distribution sense as pressure vanishes.

Convergence matches the vanishing viscosity limit for Riemann initial data.

Alternative approximation methods for cosmological models are analyzed.

Abstract

We study the limiting behavior of the solutions of Euler equations of one-dimensional compressible fluid flow as the pressure like term vanishes. This system can be thought of as an approximation for the one dimensional model for large scale structure formation of universe. We show that the solutions of former equation converges to the solution of later in the sense of distribution and agrees with the vanishing viscosity limit when the initial data is of Riemann type. A different approximation for the one dimensional model for large scale structure formation of universe is also studied.