Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption
Kenji Nakanishi, Wilhelm Schlag
TL;DR
This paper classifies the long-term behavior of solutions to the nonlinear Klein-Gordon equation in three dimensions without assuming radial symmetry, focusing on solutions with energy near the ground state.
Contribution
It extends previous radial results to the non-radial case, providing a comprehensive classification of global dynamics for solutions with energy slightly above the ground state.
Findings
Complete classification of global dynamics for non-radial solutions
Extension of previous results to non-radial symmetry
Analysis of solutions with energy near the ground state
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.
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