Solvability in weighted spaces of the three-dimensional Navier-Stokes problem in domains with cylindrical outlets to infinity - Pileckas, Konstantin (Topological Methods in Nonlinear Analysis, 2007)
The nonstationary Navier-Stokes problemis studied in a three-dimensional domain with cylindrical outletsto infinity in weighted Sobolev function spaces. The uniquesolvability of this problem is proved under natural compatibilityconditions either for a small time interval or for small data.Moreover, it is shown that the solution having prescribedfluxes over cross-sections of outlets to infinity tends in eachoutlet to the corresponding time-dependent Poiseuille flow.