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Viscous incompressible flow in unbounded domains. (English) Zbl 1012.35063
Salvi, Rodolfo (ed.), The Navier-Stokes equations: theory and numerical methods. Proceedings of the international conference, Varenna, Lecco, Italy, 2000. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 223, 87-98 (2002).
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.
For the entire collection see [Zbl 0972.00046].
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35D05 Existence of generalized solutions of PDE (MSC2000)