Nonhomogeneous boundary value problem for the time periodic linearized Navier–Stokes system in a domain with outlet to infinity

The time periodic linearized Navier–Stokes system (Stokes system) with nonhomogeneous boundary conditions is studied in a domain Ω which has a “paraboloidal” outlet to infinity. The time periodic boundary value a ( x , t ) is assumed to have a compact support and it is supposed that the flux of a over ∂Ω is nonzero. The existence and uniqueness of a weak solution is proved. The solution can have either finite or infinite Dirichlet integral depending on geometrical properties of the outlet to infinity.