Long-time existence for the semilinear Klein–Gordon equation on a compact boundary-less Riemannian manifold

DOI10.1080/03605302.2017.1278772zbMath1365.37056OpenAlexW2568261686MaRDI QIDQ2986687

Rafik Imekraz, Jean-Marc Delort

Publication date: 16 May 2017

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2017.1278772

zbMATH Keywords

Sobolev spacenormal formsemilinear Klein-Gordon equationlong-time existence

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (10)

A note on lower bound lifespan estimates for semi-linear wave/Klein-Gordon equations associated with the harmonic oscillator ⋮ Dynamics of nonlinear Klein-Gordon equations in low regularity on \(\mathbb{S}^2\) ⋮ Almost global existence for \(d\)-dimensional beam equation with derivative nonlinear perturbation ⋮ Partial normal form for the semilinear Klein-Gordon equation with quadratic potentials and algebraic non-resonant masses ⋮ Almost global existence for some Hamiltonian PDEs with small Cauchy data on general tori ⋮ A Nekhoroshev type theorem for the nonlinear Klein-Gordon equation with potential ⋮ Long-time existence for multi-dimensional periodic water waves ⋮ Long time existence results for Hamiltonian nonlinear Klein-Gordon equations on some compact manifolds ⋮ Long-time existence for semi-linear beam equations on irrational tori ⋮ Almost global existence for the nonlinear Klein-Gordon equation in the nonrelativistic limit

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