Improved Lower Bound for the Radius of Analyticity of Solutions to the fifth order KdV-BBM model

TL;DR

This paper establishes a new lower bound on the decay rate of the radius of spatial analyticity for solutions to the fifth order KdV-BBM equation, showing it cannot decay faster than 1/√t, improving previous results.

Contribution

The paper improves the known lower bound on the decay rate of the radius of analyticity from 1/t to 1/√t for solutions of the fifth order KdV-BBM equation.

Findings

The radius of analyticity decays at most like 1/√t for large t.

Previous decay bound was 1/t, now improved to 1/√t.

Results apply to solutions with initial analytic data of fixed radius.

Abstract

We show that the uniform radius of spatial analyticity $\sigma(t)$ of solutions at time $t$ to the fifth order KdV-BBM equation cannot decay faster than $1/ \sqrt{t}$ for large $t$, given initial data that is analytic with fixed radius $\sigma_0$. This improves a recent result by Belayneh, Tegegn and the third author, where they obtained a $1/t$ decay of $\sigma(t)$ for large time $t$.