Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

The swirling flow problem in boundary layer theory

This is a preview of subscription content, log in to check access.


  1. 1.

    Corduneanu, C., Sur certains systèmes différentielles non-linéaires. An. Sti. Univ. “Al. I. Cuza” Iasi, Sec. I 6, 257–260 (1960).

  2. 2.

    Hartman, P., Ordinary Differential Equations. New York: John Wiley & Sons, Inc. 1964.

  3. 3.

    Hartman, P., Unrestricted solution fields of almost separable differential equations. Trans. Amer. Math. Soc. 63, 560–580 (1948).

  4. 3a.

    Hartman, P., On the existence of similar solutions of some boundary layer problems. To appear.

  5. 4.

    Hartman, P., & N. Onuchic, On the asymptotic integration of ordinary differential equations. Pacific J. Math. 13, 1193–1207 (1963).

  6. 5.

    Hartman, P., & A. Wintner, Asymptotic integrations of linear differential equations. Amer. J. Math. 77, 45–87 (1955).

  7. 6.

    Hastings, S. P., On existence theorems for some problems from boundary layer theory. Arch. Rat. Mech. Anal. 38, 308–316 (1970).

  8. 7.

    Lan, C. C., On functional-differential equations and some laminar boundary layer problems. Thesis (The Johns Hopkins University 1971). Arch. Rat. Mech. Anal. to appear.

  9. 8.

    Lance, G. N., & M. H. Rogers, The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating disk. J. Fluid Mech. 7, 617–630 (1960).

  10. 9.

    Massera, J. L., Sur l'existence des solutions bornées et périodiques des systèmes quasilinéaires d'équations différentielles. Ann. Mat. Pure Appl. (4) 51, 95–106 (1960).

  11. 10.

    Massera, J. L., & J. J. Schäffer, Linear differential equations and functional analysis IV. Math. Ann. 139, 287–342 (1960).

  12. 11.

    McLeod, J. B., Von Kármán's swirling flow problem. Arch. Rat. Mech. Anal. 33, 91–102 (1969).

  13. 11a.

    McLeod, J. B., The asymptotic form of solutions of von Kármán's swirling flow problem. Quart. J. Math. (Oxford) (2) 20, 483–496 (1969).

  14. 11b.

    McLeod, J. B., A note on rotationally symmetric flow above an infinite rotating disc, Mathematika. To appear.

  15. 11c.

    McLeod, J. B., The existence of axially symmetric flow above a rotating disc. To appear.

  16. 12.

    McLeod, J. B., & J. Serrin, The existence of similar solutions for some laminar boundary layer problems. Arch. Rat. Mech. Anal. 31, 288–303 (1968).

  17. 13.

    Moore, F. K., Three-dimensional boundary layer theory. Advances Appl. Mech. IV, 160–228 (1956).

  18. 14.

    Serrin, J. B., Mathematical Aspects of Boundary Layer Theory. Lecture Notes, University of Minnesota 1962.

  19. 15.

    Watson, J., On the existence of solutions for a class of rotating disc flows and the convergence of successive approximations. J. Inst. Math. Applic. 1, 348–371 (1965).

Download references

Author information

Additional information

The study was supported by the Air Force Office of Scientific Research Contract No. F44620-67-C-0098.

Communicated by J. Serrin

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hartman, P. The swirling flow problem in boundary layer theory. Arch. Rational Mech. Anal. 42, 137–156 (1971).

Download citation


  • Neural Network
  • Boundary Layer
  • Complex System
  • Nonlinear Dynamics
  • Electromagnetism