On the Interior Layer Appearing in the Similarity Solutions of the Navier-Stokes Equations

Japan Journal of Industrial and Applied Mathematics

Volumn 19, Issue 2, 2002, Pages 277-300

  Nagayama, M ^a   Okamoto, H ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Boundary layer; Interior layer; Navier Stokes eqns.

Indexed keywords

EID: 0347939870     PISSN: 09167005     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03167457     Document Type: Article

References (32)

1. E.L. Allgower and K. Georg, Numerical Continuation Methods. Springer, (1990).
2. W.-J. Beyn, Numerical methods for dynamical systems. Advances in Numerical Analysis (ed. W. Light), Clarendon Press, 1991, 175-236.
3. J.F. Brady and A. Acrivos, Steady flow in a channel or tube with an accelerating surface velocity. An exact solution to the Navier-Stokes equations with reverse flow. J. Fluid Mech., 112 (1981), 127-150.
4. S.M. Cox, Analysis of steady flow in a channel with one porous wall, or with accelerating walls. SIAM J. Appl. Math., 51 (1991), 429-438.
5. W.J.F. Govaerts, Numerical Methods for Bifurcations of Dynamical Equilibria. SIAM, 2000.
6. R.E. Grundy and H.R. Allen, The asymptotic solution of a family of boundary value problems involving exponentially small terms. IMA J. Appl. Math., 53 (1994), 151-168.
7. R.E. Grundy and R. McLaughlin, Three-dimensional blow-up solutions of the Navier-Stokes equations. IMA J. Appl. Math., 63 (1999), 287-306.
8. S.P. Hastings, An existence theorem for a problem from boundary layer theory. Arch. Rat. Mech. Anal., 33 (1969), 103-109.
9. L. Howarth, Laminar boundary layers. Handbuch der Physik, VIII/1, 1959, 264-350.
10. K. Hiemenz, Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszlynder. Dinglers J., 326 (1911), 321-324, 344-348, 357-362, 372-376, 391-393, 407-410.
11. T.-W. Hwang and C.-A. Wang, On multiple solutions for Berman's problem. Proc. R. Soc. Edinburgh, 121A (1992), 219-230.
12. H. Ikeda, M. Mimura and H. Okamoto, A singular perturbation problem arising in Oseen's spiral flows. Japan J. Indust. Appl. Math., 18 (2001), 393-403.
13. H.B. Keller, Lectures on Numerical Methods in Bifurcation Theory. Tata Institute of Fun-damental Research No. 79, Springer Verlag,1987.
14. J.R. King and S.M. Cox, Asymptotic analysis of the steady-state and time-dependent Berman problem. Preprint.
15. M. Kubicek and M. Marek, Computational Methods in Bifurcation Theory and Dissipative Structure. Springer Verlag, 1983.
16. O.A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach, 1963, 32.
17. C.-C. Lan, On functional-differential equations and some laminar boundary layer problems. Arch. Rat. Mech. Anal., 42 (1971), 24-39.
18. C. Lu, A.D. MacGillivray and S.P. Hastings, Asymptotic behavior of solutions of a similarity equation for laminar flows in channels with porous walls. IMA J. Appl. Math., 49 (1992), 139-162.
19. J.B. McLeod, Laminar flow in a porous channel. Asymptotics beyond All Orders (eds. H. Segur, S. Tanveer and H. Levine), Plenum Press, 1991, 255-266.
20. M. Nagayama, H. Okamoto and J. Zhu, On the blow-up of some similarity solutions of the Navier-Stokes equations. To appear in Quaderni di Matematica.
21. H. Okamoto, Localization of singularities in inviscid limit - numerical examples. Proceedings of Navier-Stokes Equations: Theory and Numerical Methods (ed. R. Salvi), Longman, Pitman Research Notes in Mathematics Series 388, 1998, 220-236.
22. H. Okamoto and J. Zhu, Some similarity solutions of the Navier-Stokes equations and related topics. Taiwanese J. Math., 4 (2000), 65-103.
23. W.A. Robinson, The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls. J. Eng. Math., 10 (1976), 23-40.
24. K.-G. Shih, On the existence of solutions of an equation arising in the theory of laminar flow in a uniformly porous channel with injection. SIAM J. Appl. Math., 47 (1987), 526-533.
25. F.M. Skalak and C.-Y. Wang, On the nonunique solutions of laminar flow through a porous tube or channel. SIAM J. Appl. Math., 34 (1978), 535-544.
26. C.L. Taylor, W.H.H. Banks, M.B. Zaturska and P.G. Drazin, Three dimensional flow in a porous channel. Quart. J. Mech. Appl. Math., 44 (1991), 105-133.
27. C.-Y. Wang, The three-dimensional flow due to a stretching flat surface. Phys. Fluid, 27 (1984), 1915-1917.
28. E.B.B. Watson, W.H.H. Banks, M.B. Zaturska and P.G. Drazin, On transition to chaos in two-dimensional channel flow symmetrically driven by accelerating walls. J. Fluid Mech., 212 (1990), 451-485.
29. P. Watson, W.H.H. Banks, M.B. Zaturska and P.G. Drazin, Laminar channel flow driven by accelerating walls. Eur. J. Appl. Math., 2 (1991), 359-385.
30. H. Weyl, On the differential equations of the simplest boundary-layer problems. Ann. Math., 43 (1942), 381-407.
31. M.B. Zaturska, P.G. Drazin and W.H.H. Banks, On the flow of a viscous fluid driven along a channel by suction at porous walls. Fluid Dynam. Res., 4 (1988), 151-178.
32. J. Zhu, Numerical study of stagnation-point flows of incompressible fluid. Japan J. Indust. Appl. Math., 17 (2000), 209-228.