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$%I. Y. Popov, Stokeslet and the operator extensions theory, Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 1, 235258.%$

Stokeslet and the Operator Extensions Theory
Igor Yu. POPOV
Department of Higher Mathematics
Leningrad Institute of Fine Mechanics and Optics
Sablinskaya 14
197101 Leningrad USSR

Received: September 5, 1994

Operator version of the Stokeslet method in the theory of creeping flow is suggested. The approach is analogous to the zero-range potential one in quantum mechanics and is based on the theory of self-adjoint operator extensions in the space L2  and in the Pontryagin’s space with an indefinite metric. The problem of Stokes flow in two channels connected through a small opening is considered in the framework of this approach. The case of a periodic system of small openings is studied too. The picture of streamlines for such flow is obtained.

1991 Mathematics Subject Classification: 47F, 76D.