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

M. C. Lopes Filho, A. L. Mazzucato, H. J. Nussenzveig Lopes, Michael Taylor

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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.

Original languageEnglish (US)
Pages (from-to)471-513
Number of pages43
JournalBulletin of the Brazilian Mathematical Society
Volume39
Issue number4
DOIs
StatePublished - Dec 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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