Nondispersive vanishing and blow up at infinity for the energy critical nonlinear Schrödinger equation in $\mathbb {R}^3$

DOI10.1090/S1061-0022-2014-01290-3zbMath1303.35103arXiv1212.6719MaRDI QIDQ2930920

Cecilia Ortoleva, Galina Perelman

Publication date: 20 November 2014

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.6719

zbMATH Keywords

Cauchy problemground stateblow upenergy critical focusing nonlinear Schrödinger equation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44)

Related Items (6)

Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5 ⋮ Type II Blow Up Solutions with Optimal Stability Properties for the Critical Focussing Nonlinear Wave Equation on ℝ³⁺¹ ⋮ Formation of singularities in nonlinear dispersive PDEs ⋮ Construction of two-bubble solutions for some energy-critical wave equations ⋮ On stability of type II blow up for the critical nonlinear wave equation on ℝ³⁺¹ ⋮ Instability of type II blow up for the quintic nonlinear wave equation on $R^3+1$

Cites Work

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• Slow blow-up solutions for the \(H^1(\mathbb R^3)\) critical focusing semilinear wave equation
• Blow up dynamics for equivariant critical Schrödinger maps
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension

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