This talk is devoted to the 2D incompressible Euler system in presence of sources and sinks. This model dates back to Viktor Yudovich in the sixties and is an interesting example of nonlinear open system which has been widely used in controllability theory within the scope of smooth solutions. In this talk we will review how the classical issues of existence and uniqueness of weak solutions are challenged by the presence of incoming and exiting vorticity. This talk relies on two works, respectively with Marco Bravin and Florent Noisette.