Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-21T22:23:44.391Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence of solutions of Oseen type integral equations

Published online by Cambridge University Press:  17 April 2009

J.A. Belward
J.A. Belward
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Qld. 4067, AUSTRALIA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Integral equations of Oseen type are first kind Fredholm equations whose kernels have a logarithmic singularity. They arise in exterior boundary value problems in fluid flow and heat transfer. Subject to the assumption of uniqueness of solutions of the parent exterior boundary value problem, solutions of the Oseen type integral equations are shown to exist.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 1 , February 1984 , pp. 57 - 66
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Belward, J.A., “Forced convection problems and some related Fredholm integral equations of the first kind”, (Ph.D. thesis. University of Queensland, 1971).Google Scholar
[2]Carrier, G.F., Krook, M. and Pearson, C.E., Functions of a complex variable theory and technique, (McGraw Hill, New York, 1966).Google Scholar
[3]Finn, R., “On the exterior stationary problem for the Navier-Stokes equations and associated perturbation problems”. Arch. Rat. Mech. Anal., 19 (1965), 363–406.CrossRefGoogle Scholar
[4]Homentcovschi, D., “Oseen flow of a compressible fluid past a flat plate”, Quart. Appl. Math. 39 (1981), 221–237.CrossRefGoogle Scholar
[5]Jaswon, J.A. and Symm, G.T., Integral equation methods in potential theory and elastostatics, (Academic Press, London, 1977).Google Scholar
[6]Miyagi, T. and Nishioka, M., “Oseen velocity distributions in the wake of a flat plate”, J. Fluid. Mech. 97 (1980), 145–155.CrossRefGoogle Scholar
[7]olmstead, W.E. and Majumdar, S.R., “Fundamental Oseen solutions for the two-dimension flow of a micropolar fluid”, Int. J. Engng. Sc. 21 (1983), 423–433.CrossRefGoogle Scholar
[8]Rosenhead, L., Laminar boundary layers, (Clarendon Press, Oxford, 1963).Google Scholar
[9]Ursell, F., “On the exterior problems of acoustics”. Math. Proc. Comb. Phil. Soc. 74 (1973), 117–125.CrossRefGoogle Scholar
[10]Wolfe, P., “Some distribution solutions of integral equations and their application to partial differential equations”, Applicable Analysis, 1 (1971), 123–141.CrossRefGoogle Scholar