Interaction of point sources and vortices for incompressible planar fluids

In this paper we define the equations of motion for N point sources as a locally Hamiltonian vector field.We compare with the equations for N point vortices, studying first integrals and the blow up of collisions. Since it is a central vector field, it turns out that the angular momentum is identically zero; we also state our good conjecture that there exists a first integral in terms of the polar angles of the relative positions of the sources, which would imply that the system is always globally Hamiltonian. Then, we study a more general model for interaction of sources and vortices occurring simultaneously, which can be written as the sum of a Hamiltonian plus a gradient vector field. © Birkhäuser/Springer Basel AG 2010.