Formation of singularities of spherically symmetric solutions to the 3D compressible Euler equations and Euler-Poisson equations

DOI10.1007/s00030-018-0534-6zbMath1416.35197arXiv1811.07398OpenAlexW3104450945MaRDI QIDQ1729865

Yuexun Wang, Hai-liang Li

Publication date: 28 February 2019

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.07398

zbMATH Keywords

Euler equationsingularityEuler-Poisson equationslifespancompressible fluidspherically symmetric solutionlocal-in-time solutionisentropic ideal fluidweighted radial velocity

Mathematics Subject Classification ID

Initial value problems for first-order hyperbolic systems (35L45) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Euler equations (35Q31)

Related Items (10)

Non-existence of classical solutions with finite energy to the Cauchy problem of the Navier–Stokes–Korteweg equations ⋮ Optimal Decay Rates of the Compressible Euler Equations with Time-Dependent Damping in \({\mathbb {R}}^n\): (II) Overdamping Case ⋮ Global solutions for the 1-D compressible Euler equations with time-dependent damping ⋮ On the blow‐up phenomena of the compressible Navier‐Stokes‐Korteweg system with degenerate viscosity ⋮ Large time existence of Euler-Korteweg equations and two-fluid Euler-Maxwell equations with vorticity ⋮ Blowup of smooth solutions to the compressible Euler equations with radial symmetry on bounded domains ⋮ Asymptotic Behavior of Solutions to Euler Equations with Time-Dependent Damping in Critical Case ⋮ Global and blow-up solutions for compressible Euler equations with time-dependent damping ⋮ Optimal decay rates of the compressible Euler equations with time-dependent damping in \(\mathbb{R}^n\). I: Under-damping case ⋮ Formation of singularity for the classical solutions of the rotating shallow water system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compressible fluid flow and systems of conservation laws in several space variables
• Formation of singularities in solutions to nonlinear hyperbolic equations
• Development of singularities in the motion of materials with fading memory
• Formation of singularities in three-dimensional compressible fluids
• Sur l'existence des solutions locales de l'équation d'Euler-Poisson pour l'évolution d'étoiles gazeuses. (Local existence of solutions for Euler-Poisson's equation for the evolution of gazeous stars)
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differential equations
• Formation of singularities in compressible Euler-Poisson fluids with heat diffusion and damping relaxation
• Singularities of solutions to compressible Euler equations with vacuum
• Spreading of the free boundary of an ideal fluid in a vacuum
• Sur la solution à support compact de l’equation d’Euler compressible
• Sur les solution à symétrie sphérique de l’equation d’Euler-Poisson pour l’evolution d’etoiles gazeuses
• Long Time Behavior of Solutions to the 3D Compressible Euler Equations with Damping
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Non-existence of global solutions to Euler-Poisson equations for repulsive forces
• Hyperbolic Conservation Laws in Continuum Physics

This page was built for publication: Formation of singularities of spherically symmetric solutions to the 3D compressible Euler equations and Euler-Poisson equations