For some viscous incompressible flows at low Reynolds numbers we deduce a system of nonlinear integral equations for stream function and vorticity. A coating flow problem and a capillary free boundary problem are considered in details.
Mirela Kohr Ile
Babes-Bolyai University, Faculty of Mathematics
Institute of Mathematics
slow viscous flow; free surface; stream function; vorticity; integral equation; nonlinear; coating flow; capillary flow;
See the expanding block below.
C.I. Gheorghiu, M. Kohr-Ile, An integral formulation for some slow viscous flows with free surfaces, Mathematica, 36 (59) (1994), pp. 43-54.
Romanian Academy, Publishing House of the Romanian Academy
Google Scholar Profile
 E Chifu, C.I. Gheorghiu, I. Stan, Surface Mobility of Surfacant Solutions XI. Numerical Analysis for the Marangoni and the Gravity Flow in a This Liquid Layer of Triangular Section, Rev. Roumaine Chim., 29, 1 (1984) 31-42.
 C. Cuvelier, On e Computation of Free Boundaries, Research in Numerical Gluid Mechanics, (Delft 1986), 18-29, Notes Numer. Fluid Mech., 17, Vieweg, Braunschweig, 1987.
 M. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press, 1964.
 T.M. Fischer, G.C. Hsiao, W. I., Wendland, Singular Perturbations for the exterior Three-Dimensional Slow Viscous Flow Problem, J. Math. Anal. Appl. 110 (1985) 583-603.
 M.A. Kelmanson, A Direct Boundary Integral Formulation for the Oseen Flow Past a Two-Dimensional Cylinder for Arbitrary Cross-Section, Acta-Mechanica, 68 (1987), 99-119.
 M.A. Kelmanson, An Integral Equation Method for the Solution of Singular Stow Flows Problems, Journal Comp. Physics, 51 (1983), 139-158.
 M.E. O’Neil, F. Chorlton, Ideal and incompressibile fluid dynamics, Ellis Horwood, Chichester, West Sussox, 1986.
 T. Petrila, C.I. Gheorghiu, Finite Element Methods and Applications, Ed. Academiei București, 1987, (in Romanian)
 T. Petrila, M. Kohr, Some boundary techniques for viscous flows, Rev. D’Analyse Numerique et de Theorie de l’Approx., 21, 2 (1992) 167-182.
 H. Saito, I. E. Scriven, Study of Coating Flow by the finite Element Method, Journal of Comp. Physics, 42 (1981), 53-76.
 M. Van Den Tempel, Damping of Waves by Surface-Active Materials, The Journal of Chem. Physics, 42, 8 (1965), 2769-2777.