Lower bound on the radius of analyticity of solution for fifth order KdV-BBM Equation

TL;DR

This paper proves that the radius of spatial analyticity for solutions of the fifth order KdV-BBM equation cannot decay faster than 1/t over time, improving previous exponential decay bounds.

Contribution

It establishes a lower bound of 1/t decay rate for the analyticity radius, advancing understanding of solution regularity over time.

Findings

Radius of analyticity decays no faster than 1/t

Improves previous exponential decay results

Enhances understanding of solution regularity for the equation

Abstract

We show that the uniform radius of spatial analyticity $\sigma(t)$ of solution at time $t$ for the fifth order KdV-BBM equation cannot decay faster than $1/t$ for large $t>0$, given initial data that is analytic with fixed radius $\sigma_0$. This significantly improves a recent result by Carvajal and Panthee, where they established an exponential decay of $\sigma(t)$ for large $t$.