ABSTRACT
Flow problems with moving boundary are very interesting phenomena which are often found in the nature and engineering applications. These problems consist of the free surface flows ([8]), flows with interface ([3], [4], [9]) and flows in a moving domain with an assigned law ([5], [6], [7]). In this paper we consider the solvability of the two-phase problem or flow with free interface for viscous incompressible fluids in domains with noncompact boundaries. Flow problems in unbounded domains present interesting peculiar behaviour such that a particular attention was given to such a problem recently (see [1] for references). In fact posing boundary or initial-boundary value problems for the Navier-Stokes equations, it is necessary to prescribe, besides the usual boundary conditions, certain functional of the solution. This condition is connected with the possible non coincidence of certain solenoidal spaces ([1]). Due to the existence theory, a particular attention was given to this problem in the Sobolev spaces W 1,p .
