### Solvability in weighted spaces of the three-dimensional Navier-Stokes problem in domains with cylindrical outlets to infinity

#### 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.

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.

#### Keywords

Navier-Stokes equations; noncompact domains; time-dependent Poiseuille flow; existence and uniqueness of solutions

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