Viscous incompressible flow in unbounded domains (Q2771084)

The author considers the solvability of the two phase problem for flow with a free interface for a viscous incompressible fluid in a domain with noncompact boundary. Posing boundary or initial-boundary value problems for the Navier-Stokes equations, it is necessary to prescribe, besides the usual boundary conditions, certain functionals of the solution. This is a consequence of the possible noncoincidence of solenoidal spaces defined either in the distribution sense or by completion in the Sobolev space. The author first characterizes this space difference and then proves the existence of a weak solution, assuming the flow in an unbounded domain with exits to infinity and reducing the problem to one-fluid flow.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00046].