On a steady three-dimensional noncompact free boundary value problem for the Navier–Stokes equations

A steady three-dimensional flow of a viscous incompressible fluid with a noncompact free boundary above a fixed unbounded bottom is studied. It is assumed that the motion of the fluid is generated by sources and sinks situated in a bounded part of the bottom and having zero total flux. The existence for small data of the unique solution to this problem is proved and the asymptotics of the solution is constructed.