Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption

Abstract

We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy at most slightly above that of the ground state.

40 pages

References in corpus (1)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case

Cited by in corpus (6)

• Multi-solitary waves for the nonlinear Klein-Gordon equation
• Invariant Manifolds of traveling waves of the 3D Gross-Pitaevskii equation in the energy space
• Asymptotic stability near the soliton for quartic Klein-Gordon in 1D
• Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations
• On asymptotic dynamics for $L^2$ critical generalized KdV equations with a saturated perturbation
• Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus