Well-posedness for the Majda-Biello system on the half line

TL;DR

This paper establishes local well-posedness for the Majda-Biello system on the half line, extending previous results on the real line by combining Laplace transform techniques with adapted KdV boundary estimates.

Contribution

It introduces a novel approach that combines Laplace transform methods with boundary estimates to prove well-posedness for the Majda-Biello system on the half line.

Findings

Proves local well-posedness on the half line

Extends the theory from the real line to the half line

Uses combined Laplace and boundary estimate techniques

Abstract

We study the initial-boundary value problem for the Majda-Biello system posed on the right half line. We prove local well-posedness on the half line, matching the local theory on the real line established by Oh (2008). The approach combines the Laplace transform method of Bona-Sun-Zhang with adapted estimates from the work of Colliander and Kenig on the KdV half line initial-boundary value problem.