A priori estimates and analytical construction of radially symmetric solutions in the gas dynamics

TL;DR

This paper derives estimates for Riemann invariants in symmetric gas dynamics equations, enabling the construction of shock waves with controlled existence time based on initial conditions.

Contribution

It provides new C^1-a priori estimates for Riemann invariants and a method to construct shock waves in radially symmetric gas flows.

Findings

Established C^1-a priori estimates for Riemann invariants.

Constructed shock waves with existence time proportional to initial distance from the origin.

Applied estimates to spherical and cylindrical symmetry cases.

Abstract

In this article we derive C^1-a priori estimates on the Riemann invariants of the Euler compressible equations in the case of cylindrical or spherical symmetry. These estimates allow then to construct shock waves with a time of existence proportional to the distance to the origin at the initial time.