The blowup mechanism of small data solutions for the quasilinear wave equations in three space dimensions

DOI10.1007/S101140000094zbMath0989.35088OpenAlexW2163350145MaRDI QIDQ5936961

Hui Cheng Yin

Publication date: 16 July 2002

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s101140000094

zbMATH Keywords

isentropic compressible Euler equationsnonlinear hyperbolic PDEsingularity formationunfolded system

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Second-order nonlinear hyperbolic equations (35L70) Perturbations in context of PDEs (35B20) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) First-order hyperbolic systems (35L40)

Related Items (7)

The small data solutions of general 3-D quasilinear wave equations. II. ⋮ GLOBAL MULTIDIMENSIONAL SHOCK WAVE FOR THE STEADY SUPERSONIC FLOW PAST A THREE-DIMENSIONAL CURVED CONE ⋮ The Small Data Solutions of General 3D Quasilinear Wave Equations. I ⋮ Small data solutions of 2-D quasilinear wave equations under null conditions ⋮ On the blowup of classical solutions to the 3-D pressure-gradient systems ⋮ Formation and construction of a shock wave for 3-D compressible Euler equations with the spherical initial data ⋮ A global multidimensional shock wave for the steady supersonic isothermal flow

Cites Work

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• Remarques sur l'apparition de singularités dans les écoulements euleriens compressibles. (Remarks on the appearance of singularities in compressible Euler flows)
• Formation of singularities in three-dimensional compressible fluids
• Blowup of small data solutions for a quasilinear wave equation in two space dimensions.
• Lifespan and blow-up of solutions of the quasilinear wave equations in two dimensions. II
• Striated solutions of full nonlinear two-speed equations
• The blowup mechanism for 3-D quasilinear wave equations with small data
• Blowup of small data solutions for a class of quasilinear wave equations in two space dimensions. II
• Lifespan of regular solutions for axisymmetric compressible Euler equations in two dimensions
• Blowup for nonlinear hyperbolic equations
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• The blowup of solutions for 3-D axisymmetric compressible Euler equations
• Approximation Près du Temps d’Explosion des Solutions d’Équations d’Onde Quasi-Linéaires en Dimension Deux

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