Solutions of Three-Dimensional Stationary Gas Dynamics Equations

TL;DR

This paper uses symmetry methods to find exact solutions to three-dimensional stationary gas dynamics equations, revealing a broad family of solutions for different gas types and parameters.

Contribution

It introduces a novel application of symmetry methods to derive explicit and general solutions for 3D stationary gas dynamics equations, including special cases like Chaplygin gas.

Findings

General solution family for Chaplygin gas depending on three arbitrary functions

Explicit solutions for adiabatic index formulation with multiple parameters

Demonstrates the effectiveness of symmetry methods in complex gas dynamics equations

Abstract

This paper examines the three-dimensional stationary equations of a polytropic gas and employs symmetry methods to construct exact analytical solutions. In the Chaplygin gas case, the analysis yields a highly general solution family depending on three arbitrary functions, while the general adiabatic index formulation admits explicit solutions parameterized by several constants.