The Korteweg-de Vries equation on a metric star graph

We prove local well-posedness for the Cauchy problem associated with Korteweg-de Vries equation on a metric star graph with three semi-infinite edges given by one negative half-line and two positive 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 and Kenig (Commun Partial Differ Equ 27(11/12): 2187-2266, 2002), and extended by Holmer (Commun Partial Differ Equ 31:1151-1190, 2006) and Cavalcante (Differ Integral Equ 30(7/8):521-554, 2017).