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|Type:||Artigo de periódico|
|Title:||Two-dimensional incompressible viscous flow around a small obstacle|
|Abstract:||In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity omega(0) and the circulation gamma of the initial flow around the obstacle. We prove that, if gamma is sufficiently small, the limit flow satisfies the full-plane Navier-Stokes system, with initial vorticity omega(0) + gamma(d), where delta is the standard Dirac measure. The result should be contrasted with the corresponding inviscid result obtained by the authors in Iftimie et al. ( Comm. Part. Differ. Eqn. 28, 349 - 379 ( 2003)), where the effect of the small obstacle appears in the coefficients of the PDE and not only in the initial data. The main ingredients of the proof are L-p - L-q estimates for the Stokes operator in an exterior domain, a priori estimates inspired on Kato's fixed point method, energy estimates, renormalization and interpolation.|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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