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

Konstantin Pileckas

DOI: http://dx.doi.org/10.12775/TMNA.2007.014

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.

Keywords


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

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