On the Motion of a Small Light Body Immersed in a Two Dimensional Incompressible Perfect Fluid with Vorticity
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In this paper we consider the motion of a rigid body immersed in a two dimensional unbounded incompressible perfect fluid with vorticity. We prove that when the body shrinks to a massless pointwise particle with fixed circulation, the “fluid+rigid body” system converges to the vortex-wave system introduced by Marchioro and Pulvirenti (Mathematical theory of incompressible nonviscous fluids. Applied Mathematical Sciences 96, Springer-Verlag, 1994). This extends both the paper (Glass et al. Bull Soc Math France 142(3):489–536, 2014) where the case of a solid tending to a massive pointwise particle was tackled and the paper (Glass et al. Dynamics of a point vortex as limits of a shrinking solid in an irrotational fluid, 2014) where the massless case was considered but in a bounded cavity filled with an irrotational fluid.
KeywordsVorticity Normal Form Rigid Body Laurent Series Point Vortex
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