Quotient of the Euler system on one class of curves

TL;DR

This paper derives a quotient equation from the Euler system for inviscid flows along specific curves, enabling solutions via asymptotic and virial expansions, and reducing the problem to a series of ODEs.

Contribution

It introduces a novel quotient equation for the Euler system using differential invariants, simplifying the analysis of solutions along characteristic fields.

Findings

Derived the quotient equation from the Euler system.

Provided methods for solving the quotient using asymptotic and virial expansions.

Reduced the problem to a series of ordinary differential equations.

Abstract

We consider the Euler system describing a one-dimensional inviscid flows in space along curves of a certain class. Using differential invariants for the Euler system, we obtain its quotient equation. The solutions of the quotient equation that are constant along characteristic vector field provide some solutions of the Euler system. We discuss solving the quotient using asymptotic expansions of unknown functions and virial expansion of thermodynamic state equations. Thus the quotient is reduced to a series of ODE systems.