  A classical model for sources and sinks in a two-dimensional perfect
incompressible fluid occupying a bounded domain dates back to Yudovich in 1966.
  In this model, on the one hand, the normal component of the fluid velocity is
prescribed on the boundary and is nonzero on an open subset of the boundary,
corresponding either to sources (where the flow is incoming) or to sinks (where
the flow is outgoing). On the other hand the vorticity of the fluid which is
entering into the domain from the sources is prescribed.
  In this paper we investigate the existence of weak solutions to this system
by relying on \textit{a priori} bounds of the vorticity, which satisfies a
transport equation associated with the fluid velocity vector field. Our results
cover the case where the vorticity has a $L^p$ integrability in space, with $p
$ in $[1,+\infty]$, and prove the existence of solutions obtained by
compactness methods from viscous approximations. More precisely we prove the
existence of solutions which satisfy the vorticity equation in the
distributional sense in the case where $p >\frac43$, in the renormalized sense
in the case where $p >1$, and in a symmetrized sense in the case where $p =1$.
