Euler System for Compressible Fluids at a Junction

Consider n ducts having a common origin and filled with a
fluid. Along each duct, the full Euler system describes the evolution
of the fluid. 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 sufficiently small.