Abstract
The nonstationary Navier-Stokes problem is studied in a three-dimensional domain with cylindrical outlets to infinity in weighted Sobolev function spaces. The unique solvability of this problem is proved under natural compatibility conditions either for a small time interval or for small data. Moreover, it is shown that the solution having prescribed fluxes over cross-sections of outlets to infinity tends in each outlet to the corresponding time-dependent Poiseuille flow.
Citation
Konstantin Pileckas. "Solvability in weighted spaces of the three-dimensional Navier-Stokes problem in domains with cylindrical outlets to infinity." Topol. Methods Nonlinear Anal. 29 (2) 333 - 360, 2007.
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