Local solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation

TL;DR

This paper investigates the local well-posedness of the 'good' Boussinesq equation in Sobolev spaces with negative indices, expanding understanding of solution existence in less regular function spaces.

Contribution

It establishes local well-posedness results for the 'good' Boussinesq equation in Sobolev spaces with negative indices, a novel extension beyond classical positive regularity settings.

Findings

Proves local existence and uniqueness in Sobolev spaces with negative s.

Identifies the minimal regularity needed for well-posedness.

Provides new insights into the behavior of solutions with rough initial data.

Abstract

We study the local well-posedness of the initial-value problem for the nonlinear "good" Boussinesq equation with data in Sobolev spaces \textit{$H^s$} for negative indices of $s$.