Two-dimensional incompressible viscous flow around a small obstacle
| dc.creator | Iftimie, D. | |
| dc.creator | Filho, M. C. Lopes | |
| dc.creator | Lopes, H. J. Nussenzveig | |
| dc.date | 2005-09-15 | |
| dc.date.accessioned | 2026-07-07T06:31:31Z | |
| dc.date.available | 2026-07-07T06:31:31Z | |
| dc.description | 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 $ω_0$ and the circulation $γ$ of the initial flow around the obstacle. We prove that, if $γ$ is sufficiently small, the limit flow satisfies the full-plane Navier-Stokes system, with initial vorticity $ω_0 + γδ$, where $δ$ is the standard Dirac measure. The result should be contrasted with the corresponding inviscid result obtained by the authors in [Comm P.D.E. 28 (2003) 349-379], where the effect of the small obstacle appears in the coefficients of the PDE and not only on 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. | |
| dc.identifier | https://arxiv.org/abs/math/0509354 | |
| dc.identifier | http://arxiv.org/abs/math/0509354 | |
| dc.identifier | Math. Ann. v. 336 (2006), 449-489 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98627 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q30 (Primary) 76D05 (Secondary) | |
| dc.title | Two-dimensional incompressible viscous flow around a small obstacle | |
| dc.type | text |