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We consider Leray's problem on stationary Navier0Stokes flows with arbitrary large fluxes in an unbounded cylinder with several exits to infinity. For a stationary Navier-Stokes flow with large fluxes in the unbounded cylinder, we prove that, if the difference between the pressure of the main flow and the pressure of the Poiseuille flow with the same flux in a branch of the cylinder remains bounded at vertical bar x vertical bar -> infinity, then the flow behaves at infinity of the branch like the Poiseuille flow.

A remark on Leray’s problem on stationary Navier–Stokes flows with large fluxes in infinite cylindrical domains