Scattering of rough solutions of the nonlinear Klein-Gordon equations in 3D

TL;DR

This paper proves scattering for solutions of the 3D nonlinear Klein-Gordon equation with sub-energy initial data, using decay estimates and frequency decomposition techniques.

Contribution

It introduces a novel decay estimate in H^{s} for s<1, enabling scattering results below the energy norm for 3D Klein-Gordon equations.

Findings

Proved scattering for 3D Klein-Gordon with 3<p<5.

Developed exponential decay estimates in fractional Sobolev spaces.

Utilized low-high frequency decomposition for analysis.

Abstract

We prove scattering of solutions below the energy norm of the 3D Klein-Gordon equation for 5>p>3. In order to do that, we generate an exponential-type decay estimate in H^{s}, s<1, by means of concentration and a low-high frequency decomposition.