Euler system for compressible fluids at a junction

Consider n ducts having a common origin and. lled with a. uid. Along each duct, the full Euler system describes the evolution of the. uid. At the junction, suitable physical conditions couple the n Euler systems. In this paper we prove the well posedness of the Cauchy problem for the model so obtained, provided the total varaiatio of the initial data is su. ciently small.