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

摘要

We consider Leray's problem on stationary Navier-Stokes flows with arbitrarylarge fluxes in an unbounded cylinder with several exits to infinity. For astationary Navier-Stokes flow with large fluxes in the unbounded cylinder weprove that, if the difference between the pressure of the main flow and thepressure of the Poiseuille flow with the same flux in a branch of the cylindersatisfies some asymptotic boundedness condition at $|x|ightarrow infty$ thenthe flow behaves at infinity of the branch like the Poiseuille flow.