Two existence results for the vortex-wave system
Received: 20 October 2010
Accepted: 8 November 2010
Mathematics Subject Classification (2000): 35Q35, 76B03, 76B47.
Keywords: Two-dimensional Euler equations, incompressible flows, global existence of weak solutions, point vortices, vortex sheets.
Abstract: The vortex-wave system is a coupling of the two-dimensional Euler equations for the vorticity together with the point vortex system. It was introduced by C. Marchioro and M. Pulvirenti   to modelize the evolution of a finite number of concentrated vortices moving in a bounded vorticity background. The purpose of this paper is to provide global existence of a solution in two cases where the background vorticity is not bounded. Part of this work is joint with M. C. Lopes Filho and H. J. Nussenzveig Lopes.
 C. Marchioro and M. Pulvirenti, On the vortex-wave system,
in ''Mechanics, analysis, and geometry: 200 years after Lagrange'',
North-Holland Publishing Co., Amsterdam 1991, 79-95.
 C. Marchioro and M. Pulvirenti, Mathematical theory of incompressible nonviscous fluids, Springer-Verlag, New York 1994.