Revisited bilinear Schr\"{o}dinger estimates with applications to generalized Boussinesq equations

TL;DR

This paper enhances the understanding of generalized Boussinesq equations by improving bilinear Schrödinger estimates and introducing an automated method for summation arguments, leading to better local well-posedness results.

Contribution

It provides improved bilinear estimates for Schrödinger equations and introduces a new automated approach for summation, advancing the analysis of generalized Boussinesq equations.

Findings

Enhanced bilinear estimates for Schrödinger equations.

Automated summation procedure for bounds.

Improved local well-posedness results.

Abstract

In this paper, our goal is to improve the local well-posedness theory for certain generalized Boussinesq equations by revisiting bilinear estimates related to the Schr\"{o}dinger equation. Moreover, we propose a novel, automated procedure to handle the summation argument for these bounds.