TY - JOUR

T1 - Vanishing viscosity limits and boundary layers for circularly symmetric 2D flows

AU - Lopes Filho, M. C.

AU - Mazzucato, A. L.

AU - Nussenzveig Lopes, H. J.

AU - Taylor, Michael

N1 - Funding Information:
Received 20 March 2008. *Supported in part by CNPq grant 302.102/2004-3. **Supported in part by NSF grant DMS-0405803. ***Supported in part by CNPq grant 302.214/2004-6. ****Supported in part by NSF grant DMS-0456861.

PY - 2008/12

Y1 - 2008/12

N2 - We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [10] on the vanishing viscosity limit of circularly symmetric viscous flow in a disk with rotating boundary, shown there to converge to the inviscid limit in L 2-norm as long as the prescribed angular velocity α(t) of the boundary has bounded total variation. Here we establish convergence in stronger L 2 and L p -Sobolev spaces, allow for more singular angular velocities α, and address the issue of analyzing the behavior of the boundary layer. This includes an analysis of concentration of vorticity in the vanishing viscosity limit. We also consider such flows on an annulus, whose two boundary components rotate independently.

AB - We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [10] on the vanishing viscosity limit of circularly symmetric viscous flow in a disk with rotating boundary, shown there to converge to the inviscid limit in L 2-norm as long as the prescribed angular velocity α(t) of the boundary has bounded total variation. Here we establish convergence in stronger L 2 and L p -Sobolev spaces, allow for more singular angular velocities α, and address the issue of analyzing the behavior of the boundary layer. This includes an analysis of concentration of vorticity in the vanishing viscosity limit. We also consider such flows on an annulus, whose two boundary components rotate independently.

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U2 - 10.1007/s00574-008-0001-9

DO - 10.1007/s00574-008-0001-9

M3 - Article

AN - SCOPUS:58149265078

VL - 39

SP - 471

EP - 513

JO - Bulletin of the Brazilian Mathematical Society

JF - Bulletin of the Brazilian Mathematical Society

SN - 1678-7544

IS - 4

ER -