Sharp threshold of global existence for the Klein-Gordon equations with critical nonlinearity

DOI10.1007/S10255-007-7085-7zbMath1180.35362OpenAlexW2067618896MaRDI QIDQ844060

Jian Zhang, Bo-ling Guo, Zai-Hui Gan

Publication date: 18 January 2010

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

Full work available at URL: https://doi.org/10.1007/s10255-007-7085-7

zbMATH Keywords

Klein-Gordon equationglobal existencesharp thresholdtwo space dimensionscross-constrained variational problem

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) NLS equations (nonlinear Schrödinger equations) (35Q55) Initial value problems for second-order hyperbolic equations (35L15) Blow-up in context of PDEs (35B44) Second-order semilinear hyperbolic equations (35L71)

Related Items (3)

Unstable ground state and blow up result of nonlocal Klein-Gordon equations ⋮ Global existence and blow up of the solution for nonlinear Klein-Gordon equation with general power-type nonlinearities at three initial energy levels ⋮ Global existence and blow up of the solution for nonlinear Klein-Gordon equation with variable coefficient nonlinear source term

Cites Work

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• Saddle points and instability of nonlinear hyperbolic equations
• On existence and scattering for critical and subcritical nonlinear Klein-Gordon equations in Hs
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• On the standing wave in coupled non-linear Klein-Gordon equations
• Sharp Threshold for Blowup and Global Existence in Nonlinear Schrödinger Equations Under a Harmonic Potential
• Sharp conditions of global existence for nonlinear Schrödinger and Klein-Gordon equations.

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