Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows

Details Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows

2007-09-13

arxiv.org/abs/0709.2056v1

Bull. Braz. Math. Soc. v. 39 (2008), 471-513

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00574-008-0001-9

We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [LMN], 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 $\alpha(t)$ 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 $\alpha$, 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. [LMN] Lopes Filho, M. C., Mazzucato, A. L. and Nussenzveig Lopes, H. J., Vanishing viscosity limit for incompressible flow inside a rotating circle, preprint 2006.

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