Abstract
The vortex-wave system is a coupling of the two-dimensional vorticity equation with the point-vortex system. It is a model for the motion of a finite number of concentrated vortices moving in a distributed vorticity background. In this article, we prove existence of a weak solution to this system with an initial background vorticity in L p, p>2, up to the time of first collision of point vortices.
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Communicated by P. Newton.
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Lopes Filho, M.C., Miot, E. & Nussenzveig Lopes, H.J. Existence of a Weak Solution in L p to the Vortex-Wave System. J Nonlinear Sci 21, 685–703 (2011). https://doi.org/10.1007/s00332-011-9097-y
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DOI: https://doi.org/10.1007/s00332-011-9097-y