Singularity formation for the supersonic inward wave of compressible Euler equations with radial symmetry

2025/11/19 by Chen, Geng, El-Katri, Faris A., Hu, Yanbo +1
Mathematics · Physics and Astronomy · Engineering · #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.2511.15180

Abstract

In this paper, we consider the singularity formation of smooth solutions for the compressible radially symmetric Euler equations. By applying the characteristic method and the invariant domain idea, we show that, for polytropic ideal gases with γ≥3, the smooth solution develops a singularity in finite time for a class of initial supersonic inward waves.

Citations

• Global solution and singularity formation for the supersonic expanding wave of compressible Euler equations with radial symmetry
• A new type of stable shock formation in gas dynamics
• A characteristics approach to shock formation in 2D Euler with azimuthal symmetry and entropy
• Shock formation and vorticity creation for 3d Euler
• Singularity formation for radially symmetric expanding wave of Compressible Euler Equations
• Formation of point shocks for 3D compressible Euler
• Formation of shocks for 2D isentropic compressible Euler
• The Shock Development Problem
• Shock formation in solutions to the 2D compressible Euler equations in\n the presence of non-zero vorticity
• Optimal time-dependent lower bound on density for classical solutions of 1-D compressible Euler equations
• Compressible Flow and Euler's Equations
• Shock formation in the compressible Euler equations and related systems
• Shock-free Solutions of the Compressible Euler Equations
• Formation of singularities in one‐dimensional nonlinear wave propagation

Related

• Global solution and singularity formation for the supersonic expanding wave of compressible Euler equations with radial symmetry
• Singularity formation for radially symmetric expanding wave of Compressible Euler Equations
• Formation of singularity and smooth wave propagation for the non-isentropic compressible Euler equations
• Singularities of solutions to compressible Euler equations with vacuum
• Singularity formation for the compressible Euler equations with general pressure law