# Global Entropy Solutions to the Gas Flow in General Nozzle

## TL;DR

This paper proves the global existence of entropy solutions for gas flow in nozzles with general cross-sections, using vanishing viscosity and compactness methods, without small initial data assumptions.

## Contribution

It introduces new viscosity techniques and applies the vanishing viscosity method to establish global solutions for Euler equations in complex nozzle geometries.

## Key findings

- Existence of entropy solutions is proven for general nozzle geometries.
- Solutions are uniformly bounded independently of time.
- No smallness condition on initial data is required.

## Abstract

We are concerned with the global existence of entropy solutions for the compressible Euler equations describing the gas flow in a nozzle with general cross-sectional area, for both isentropic and isothermal fluids. New viscosities are delicately designed to obtain the uniform bound of approximate solutions. The vanishing viscosity method and compensated compactness framework are used to prove the convergence of approximate solutions. Moreover, the entropy solutions for both cases are uniformly bounded independent of time. No smallness condition is assumed on initial data. The techniques developed here can be applied to compressible Euler equations with general source terms.