Riv. Mat. Univ. Parma, Vol. 3, No. 1, 2012

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. MathSciNet

[8] C. Marchioro and M. Pulvirenti, Mathematical theory of incompressible nonviscous fluids, Springer-Verlag, New York 1994. MathSciNet

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