Nonstationary flow for the Navier-Stokes equations in a cylindrical pipe
  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 in $W^{2,1}_2.$ 
Joanna Renclawowicz and Wojciech M. Zajaczkowski
math.AP math-ph math.MP