On the Benjamin Ono equation in the half line

TL;DR

This paper investigates the initial-boundary value problem for the Benjamin-Ono equation on the half line, focusing on the global existence of solutions and extending previous work on asymptotic behavior.

Contribution

It extends prior research by analyzing the global in time existence of solutions for the Benjamin-Ono equation with boundary conditions on the half line.

Findings

Established conditions for global existence of solutions

Extended understanding of asymptotic behavior for large time

Built upon previous work by Hayashi and Kaikina

Abstract

We consider the inhomogeneous Dirichlet initial boundary value problem for the Benjamin-Ono equation formulated on the half line. We study the global in time existence of solutions to the initial-boundary value problem. This work is a continuation of the ones [14,15] by Hayashi and Kaikina where the global in time existence and the asymptotic behaviour of solutions for large time were considered.