Solvability in weighted spaces of the three-dimensional Navier-Stokes problem in domains with cylindrical outlets to infinity
KeywordsNavier-Stokes equations, noncompact domains, time-dependent Poiseuille flow, existence and uniqueness of solutions
AbstractThe 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.
How to Cite
PILECKAS, Konstantin. Solvability in weighted spaces of the three-dimensional Navier-Stokes problem in domains with cylindrical outlets to infinity. Topological Methods in Nonlinear Analysis [online]. 1 June 2007, T. 29, nr 2, s. 333–360. [accessed 19.9.2021].
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