Vanishing viscosity limits for a class of circular pipe flows. (English) Zbl 1220.35121

Mazzucato, Anna; Taylor, Michael

Commun. Partial Differ. Equations 36, No. 1-3, 328-361 (2011).

Authors’ abstract: We consider 3D Navier-Stokes flows with no-slip boundary condition in an infinitely long pipe with circular cross section. The velocity fields we consider are independent of the variable parametrizing the axis of the pipe, and the component of the velocity normal to the axis is arranged to be circularly symmetric, though we impose no such symmetry on the component of velocity parallel to the axis. For such flows we analyze the limit as the viscosity tends to zero, including boundary layer estimates.

Reviewer: Miloš Čanak (Beograd)

MSC:

35Q30	Navier-Stokes equations
35K20	Initial-boundary value problems for second-order parabolic equations
35B25	Singular perturbations in context of PDEs
76D10	Boundary-layer theory, separation and reattachment, higher-order effects

Keywords:

boundary layer; Navier-Stokes equations; singular perturbation; viscosity

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