부산대학교 도서관

We construct a time-dependent conformal map parameterizing a growing, doubly-periodic blob of viscous fluid of infinite connectivity formed by injection into an initially empty Hele-Shawcell through an array of point sources, assuming zero-surface tension along the free boundaries of the blob. The map is from a preimage circular domain. It is identified as a function that is quasi-automorphic with respect to an associated secondary Schottky group and then constructed explicitly in terms of the Schottky-Klein prime function. A key role in this construction is played by the Schwarz function of the free boundary. Additional possible applications of these results include Hele-Shaw flows in the interior of bounded domains, quasi-steady Stokes flows and quadrature domain theory. [ABSTRACT FROM AUTHOR]