Mathematica Eterna
Open Access

Abstract

Singularity formation of compressible Euler equations with source term

Ran Guo and Mengmeng Shang

In this paper, we mainly study the blow-up of classical solutions to one-dimensional compressible Euler equations with source term. We discussed separately the cases of source term with Riemann invariants and Riemann invariants function. The method we adopted here is to reduce the system to a diagonal form system by introducing the Riemann invariant. Then, we proved the solution blow-up in a finite time when the initial data satisfy certain conditions.