Global well-posedness for the nonlinear wave equation in analytic Gevrey spaces

TL;DR

This paper investigates how the spatial analyticity radius of solutions to the nonlinear wave equation decays over time, providing an asymptotic rate of decay for initial data in analytic Gevrey spaces.

Contribution

It establishes an asymptotic decay rate for the analyticity radius of solutions in Gevrey spaces, advancing understanding of solution regularity over time.

Findings

Derived an explicit asymptotic decay rate for the analyticity radius.

Extended the analysis of nonlinear wave equations to Gevrey space initial data.

Provided insights into the long-term regularity of solutions.

Abstract

We obtain an asymptotic rate of decay for the radius of spatial analyticity of solutions to the nonlinear wave equation with initial data in the analytic Gevrey spaces.