Blow-up of the radially symmetric solutions for the quadratic nonlinear Schrödinger system without mass-resonance

DOI10.1016/j.na.2020.111895zbMath1470.35334arXiv1810.09153OpenAlexW3018784559MaRDI QIDQ2188526

Nobu Kishimoto, Takahisa Inui, Kuranosuke Nishimura

Publication date: 11 June 2020

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09153

zbMATH Keywords

blow-upradial symmetrygrow-upvirial identityquadratic Schrödinger systemmass-resonance

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Resonance in context of PDEs (35B34) Blow-up in context of PDEs (35B44) Symmetries, invariants, etc. in context of PDEs (35B06) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (10)

Blow-up solutions for a system of Schrödinger equations with general quadratic-type nonlinearities in dimensions five and six ⋮ On a system of nonlinear Schrödinger equations with quadratic interaction and L2-critical growth ⋮ Global dynamics below the ground state for the focusing Schrödinger equation with a potential ⋮ Traveling waves for a nonlinear Schrödinger system with quadratic interaction ⋮ Global well-posedness for the Sobolev critical nonlinear Schrödinger system in four space dimensions ⋮ Blow-up results for systems of nonlinear Schrödinger equations with quadratic interaction ⋮ Scattering for the 5D quadratic NLS system without mass-resonance ⋮ Scattering for quadratic-type Schrödinger systems in dimension five without mass-resonance ⋮ A system of Schrödinger equations with general quadratic-type nonlinearities ⋮ Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with χ³ nonlinear response

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