We consider the Euler equations for compressible fluids
in a nozzle whose cross-section is variable and may contain discontinuities.
We view these equations as a hyperbolic system in nonconservative form
and investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [J. Math. Pures Appl.
74 (1995) 483–548].
Observing that the entropy equality has a fully conservative form,
we derive a minimum entropy principle satisfied by entropy solutions.
We then establish the stability of a class of numerical approximations for this system.