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

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.

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
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