New long time existence results for a class of Boussinesq-type systems

TL;DR

This paper establishes improved long-term existence results for a class of Boussinesq-type systems modeling long wave, small amplitude gravity surface waves, using an energy method on spectrally localized equations.

Contribution

It introduces a novel energy method approach that enhances regularity requirements for solving Boussinesq systems over large time scales.

Findings

Achieved better regularity thresholds for long time existence.

Extended previous results on Boussinesq systems.

Demonstrated the effectiveness of spectral localization in energy estimates.

Abstract

In this paper we deal with the long time existence for the Cauchy problem associated to some asymptotic models for long wave, small amplitude gravity surface waves. We generalize some of the results that can be found in the literature devoted to the study of Boussinesq systems by implementing an energy method on spectrally localized equations. In particular, we obtain better results in terms of the regularity level required to solve the initial value problem on large time scales.