# The Korteweg-de Vries equation on a metric star graph

## TL;DR

This paper establishes local well-posedness for the Korteweg-de Vries equation on a star graph with three edges, extending low regularity analysis techniques to this geometric setting.

## Contribution

It introduces a framework for analyzing the Korteweg-de Vries equation on a star graph with specific boundary conditions using the Duhamel Boundary Forcing Operator.

## Key findings

- Proves local well-posedness in low regularity spaces.
- Extends boundary forcing techniques to star graph geometries.
- Handles mixed boundary conditions at the vertex.

## Abstract

We prove local well-posedness for the Cauchy problem associated to Korteweg-de Vries equation on a metric star graph with three semi-infinite edges given by one negative half-line and two positives half-lines attached to a common vertex, for two classes of boundary conditions. The results are obtained in the low regularity setting by using the Duhamel Boundary Forcing Operator, in context of half-lines, introduced by Colliander, Kenig (2002),and extended by Holmer (2006) and Cavalcante (2017).