Abstract
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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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.
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Lopes Filho, M.C., Mazzucato, A.L., Nussenzveig Lopes, H.J. et al. Vanishing viscosity limits and boundary layers for circularly symmetric 2D flows. Bull Braz Math Soc, New Series 39, 471–513 (2008). https://doi.org/10.1007/s00574-008-0001-9
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DOI: https://doi.org/10.1007/s00574-008-0001-9