Global solvability for a large flux of a three-dimensional time-dependent Navier-Stokes problem in a straight cylinder

The unique global existence of a solution to nonstationary Navier-Stokes system with prescribed nonzero flux F(t) in an infinite threedimensional pipe is proved. The obtained solution remains close to the corresponding nonstationary Poiseuille flow. Moreover, it converges to the Poiseuille flow as |x3|(right arrow)(infinity).