On the radius of spatial analyticity for the 1d Dirac-Klein-Gordon equations

TL;DR

This paper investigates how the radius of spatial analyticity of solutions to the 1D Dirac-Klein-Gordon equations diminishes over time, establishing a lower bound on its decay rate.

Contribution

It proves that the radius of analyticity cannot decay faster than a polynomial rate of 1/t^4 for solutions over time.

Findings

Radius of analyticity decays at most as 1/t^4

Solutions remain analytic in a shrinking strip over time

Provides bounds on the decay rate of analyticity

Abstract

We study the well-posedness of the Dirac-Klein-Gordon system in one space dimension with initial data that have an analytic extension to a strip around the real axis. It is proved that the radius of analyticity of the solutions at time $t$ cannot decay faster than $1/t^4$ as $t$ tends to infinity.