A criterion of singularity formation for the non-isentropic gas dynamics equations

TL;DR

This paper establishes precise conditions on initial data that determine whether solutions to 1D non-isentropic gas dynamics equations develop singularities or remain smooth over time.

Contribution

It provides necessary and sufficient criteria for blow-up and identifies initial data classes leading to global smooth solutions.

Findings

Derived exact conditions for singularity formation.

Characterized initial data leading to global smooth solutions.

Established a method to determine solution behavior from initial conditions.

Abstract

For the 1D non-isentropic polytropic gas dynamics equations we find sufficient and necessary conditions for blow up of derivatives in the terms of Cauchy data. In particular, the method allows to determine exact class of initial data corresponding to globally smooth in time solution.