Interaction of vortices in viscous planar flows - Mathematics > Analysis of PDEsReportar como inadecuado




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Abstract: We consider the inviscid limit for the two-dimensional incompressibleNavier-Stokes equation in the particular case where the initial flow is afinite collection of point vortices. We suppose that the initial positions andthe circulations of the vortices do not depend on the viscosity parameter u,and we choose a time T > 0 such that the Helmholtz-Kirchhoff point vortexsystem is well-posed on the interval 0,T. Under these assumptions, we provethat the solution of the Navier-Stokes equation converges, as u -> 0, to asuperposition of Lamb-Oseen vortices whose centers evolve according to aviscous regularization of the point vortex system. Convergence holds uniformlyin time, in a strong topology which allows to give an accurate description ofthe asymptotic profile of each individual vortex. In particular, we compute toleading order the deformations of the vortices due to mutual interactions. Thisallows to estimate the self-interactions, which play an important role in theconvergence proof.



Autor: Thierry Gallay

Fuente: https://arxiv.org/







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