On the nonstationary linearized Navier-Stokes problem in domains with cylindrical outlets to infinity
The author examines the nonstationary linearized Navier-Stokes system in a domain with cylindrical outlets to infinity in weighted function spaces with exponential weight functions. It is proved that under natural compatibility conditions on the external force there exists a unique solution with prescribed non-zero fluxes over the sections of outlets that exponentially tends in each outlet to the corresponding nonstationary Poiseuille flow. The proof is based on estimates of the solution obtained by using the weighted Friedrichs inequality, on the Galerkin method, and on solvability and estimates of the solution gradient for the divergence equation.
scientific article; zbMATH DE number 2172742
scientific article