[8] C. Marchioro and M. Pulvirenti, Mathematical theory of incompressible nonviscous fluids, Springer-Verlag, New York 1994.
Evelyne Miot
Two existence results for the vortex-wave system
Pages: 131-146
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 [7] [8] 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.
[7] 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.
[8] C. Marchioro and M. Pulvirenti, Mathematical theory of incompressible nonviscous fluids,
Springer-Verlag, New York 1994.