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In cylindrical domain, we consider the nonstationary flow with prescribed inflow and outflow, modelled with Navier–Stokes equations under the slip boundary conditions. Using smallness of some derivatives of inflow function, external force and initial velocity of the flow, but with no smallness restrictions on the inflow, initial velocity neither force, we prove existence of solutions inW    2    2  ,  1    . Copyright © 2012 John Wiley & Sons, Ltd.

Nonstationary flow for the Navier–Stokes equations in a cylindrical pipe