On the periodic "good" Boussinesq equation

TL;DR

This paper investigates the well-posedness of the periodic nonlinear "good" Boussinesq equation, establishing local well-posedness for initial data in Sobolev spaces with regularity above -1/4, matching the real case results.

Contribution

It extends the well-posedness results for the periodic "good" Boussinesq equation to Sobolev spaces with regularity s > -1/4, aligning with known results for the real case.

Findings

Proves local well-posedness for s > -1/4 in Sobolev spaces

Matches the regularity range of the real case

Extends understanding of the periodic "good" Boussinesq equation

Abstract

We study the well-posedness of the initial-value problem for the periodic nonlinear "good" Boussinesq equation. We prove that this equation is local well-posed for initial data in Sobolev spaces \textit{$H^s(\T)$} for $s>-1/4$, the same range of the real case obtained in Farah \cite{LG4}.