Global well-posedness for a family of regularized Benjamin-type equations

TL;DR

This paper establishes local and global well-posedness for a family of regularized Benjamin-type equations in various Sobolev spaces, advancing understanding of their mathematical properties.

Contribution

It provides the first comprehensive proof of well-posedness for this family of equations in both periodic and nonperiodic settings.

Findings

Proved local well-posedness in Sobolev spaces.

Established global well-posedness under certain conditions.

Applicable to both periodic and nonperiodic cases.

Abstract

In this work we prove local and global well-posedness results for the Cauchy problem of a family of regularized nonlinear Benjamin-type equations in both periodic and nonperiodic Sobolev spaces.