A lower bound for the life span of solutions to the Kirchhoff equation with Gevrey data

TL;DR

This paper establishes a new lower bound for the lifespan of solutions to the Kirchhoff equation with Gevrey initial data, especially improving classical bounds when initial data frequency is concentrated at zero.

Contribution

It introduces a refined lower bound for solution lifespan of the Kirchhoff equation with Gevrey data, enhancing previous results in specific spectral cases.

Findings

New lower bound for solution lifespan established

Improvement over classical bounds for concentrated initial spectrum

Applicable to initial data in Gevrey spaces

Abstract

We provide a new lower bound for the life span of solutions to the Kirchhoff equation for which the initial data belongs to the Gevrey space. This lower bound strictly improves the classical one in the case when the frequency spectrum of the initial data is concentrated at the origin.