 09140 Thierry Gallay
 Interaction of vortices in viscous planar flows
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Aug 18, 09

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Abstract. We consider the inviscid limit for the twodimensional
incompressible NavierStokes equation in the particular case where
the initial flow is a finite collection of point vortices. We
suppose that the initial positions and the circulations of the
vortices do not depend on the viscosity parameter $\nu$, and we
choose a time $T > 0$ such that the HelmholtzKirchhoff point vortex
system is wellposed on the interval $[0,T]$. Under these
assumptions, we prove that the solution of the NavierStokes
equation converges, as $\nu \to 0$, to a superposition of LambOseen
vortices whose centers evolve according to a viscous regularization
of the point vortex system. Convergence holds uniformly in time, in
a strong topology which allows to give an accurate description of
the asymptotic profile of each individual vortex. In particular, we
compute to leading order the deformations of the vortices due to
mutual interactions. This allows to estimate the selfinteractions,
which play an important role in the convergence proof.
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