Blow-up Phenomena for Compressible Euler Equations with Non-vacuum Initial Data

TL;DR

This paper investigates the conditions under which solutions to the compressible Euler equations with non-vacuum initial data develop singularities, providing new initial value blowup criteria applicable in multiple dimensions and symmetries.

Contribution

It introduces novel blowup conditions for the compressible Euler equations that apply to a broad class of initial data and includes results for 1D non-radial cases.

Findings

Established new initial blowup conditions for compressible Euler equations.

Extended blowup results to 1D non-radial symmetry cases.

Covered a general class of testing functions for blowup analysis.

Abstract

In this article, we study the blowup phenomena of compressible Euler equations with non-vacuum initial data. Our new results, which cover a general class of testing functions, present new initial value blowup conditions. The corresponding blowup results of the 1-dimensional case in non-radial symmetry are also included.