Instability of type II blow up for the quintic nonlinear wave equation on $R^3+1$

DOI10.24033/bsmf.2690zbMath1320.35220arXiv1212.4628OpenAlexW1890531207MaRDI QIDQ5255631

Joachim Krieger, Joules Nahas

Publication date: 16 June 2015

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.4628

zbMATH Keywords

scatteringinvariant manifoldhyperbolic dynamicscritical wave equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Initial value problems for second-order hyperbolic equations (35L15) Blow-up in context of PDEs (35B44) Second-order semilinear hyperbolic equations (35L71)

Related Items (5)

Blow up dynamics for the hyperbolic vanishing mean curvature flow of surfaces asymptotic to the Simons cone ⋮ Stable blowup for wave equations in odd space dimensions ⋮ Global solutions with asymptotic self-similar behaviour for the cubic wave equation ⋮ Dynamics of the focusing critical wave equation ⋮ Center-stable manifold of the ground state in the energy space for the critical wave equation

Cites Work

• Nonscattering solutions and blowup at infinity for the critical wave equation
• Slow blow-up solutions for the \(H^1(\mathbb R^3)\) critical focusing semilinear wave equation
• Smooth type II blow-up solutions to the four-dimensional energy-critical wave equation
• Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation
• Classification of the radial solutions of the focusing, energy-critical wave equation
• Threshold phenomenon for the quintic wave equation in three dimensions
• Full range of blow up exponents for the quintic wave equation in three dimensions
• Global dynamics away from the ground state for the energy-critical nonlinear wave equation
• The instability of Bourgain-Wang solutions for the <i>L</i><sup xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> critical NLS
• Nondispersive vanishing and blow up at infinity for the energy critical nonlinear Schrödinger equation in $\mathbb {R}^3$
• Stable Blowup Dynamics for the 1‐Corotational Energy Critical Harmonic Heat Flow
• On the focusing critical semi-linear wave equation
• Stable blow up dynamics for energy supercritical wave equations

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