Solvability of boundary and initial-boundary value problems for the Navier-Stokes equations in domains with noncompact boundaries

One considers boundary and Initial-boundary value problems for Navier-Stokes equations in domains with several “outlets” at infinity. It is shown that if one prescribes the limiting values of the pressure at infinity in those “outlets” which expand sufficiently fast, then these problems are solvable in the class of vectors with a finite Dirichlet integral.