On the solvability of boundary and initial-boundary value problems for the Navier-Stokes system in domains with noncompact boundaries

Abstract

In the present paper the solvability of boundary value problems for the Stokes and Navier-Stokes equations is proved for noncompact domains with several "exits" to infinity. In these problems the velocity satisfies usual boundary conditions and has a bounded Dirichlet integral and the pressure has prescribed limiting values at infinity in some "exits".