Singularity formation for the compressible Euler equations with general pressure law

TL;DR

This paper investigates how classical solutions to the compressible Euler equations with general pressure laws develop singularities, demonstrating gradient blow-up without smallness assumptions using Riccati equations and density estimates.

Contribution

It provides a novel analysis of singularity formation in compressible Euler equations with general pressure laws, removing smallness constraints.

Findings

Gradient blow-up occurs without smallness assumptions.

New estimates establish upper bounds for density.

Analysis relies on Riccati type equations.

Abstract

In this paper, the singularity formation of classical solutions for the compressible Euler equations with general pressure law is considered. The gradient blow-up of classical solutions is shown without any smallness assumption by the delicate analysis on the decoupled Riccati type equations. The proof also relies on a new estimate for the upper bound of density.