Singular perturbation theory: A viscous flow out of Göttingen

Annual Review of Fluid Mechanics

Volumn 42, Issue , 2010, Pages 1-17

  O'Malley, Robert E ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Boundary layers; History; Singular perturbations

Indexed keywords

APPLIED MATHEMATICS; SINGULAR PERTURBATION THEORY; SINGULAR PERTURBATIONS;

BOUNDARY LAYERS;

PERTURBATION TECHNIQUES;

BOUNDARY LAYER; FLUID DYNAMICS; MATHEMATICAL THEORY; NUMERICAL METHOD; VISCOUS FLOW;

EID: 77952813773     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.fluid.060909.133212     Document Type: Review

References (82)

1. Ackroyd JAD, Axcell BP, Ruban AJ. 2001. Early Developments of Modern Aerodynamics. Oxford: Butterworth-Heinemann
2. Anderson JD Jr. 2005. Ludwig Prandtl's boundary layer. Phys. Today 58:42-48
3. Batchelor G. 1996. The Life and Legacy of G. I. Taylor. Cambridge, UK: Cambridge Univ. Press
4. Beyerchen A. 1977. Scientists Under Hitler, Politics and the Physics Community in the Third Reich. New Haven, CT: Yale Univ. Press
5. Birkhoff GD. 1908. On the asymptotic character of the solutions of certain linear differential equations containing a parameter. Trans. Am. Math. Soc. 9:219-231
6. Birkhoff GD. 1938. Fifty years of American mathematics. In Semicentennial Addresses of the American Mathematical Society, 2:270-315. New York: Am. Math. Soc.
7. Blasius H. 1908. Grenzschlichten in Flüssigkeiten mit Kleiner Reibung. Z. Math. Phys. 56:1-37
8. Cesari L, Kannan R, Weinberger H, eds. 1978. Nonlinear Analysis: A Collection of Papers in Honor of Erich H. Rothe. New York: Academic
9. Chang KW, Howes FA. 1984. Nonlinear Singular Perturbation Phenomena: Theory and Application. New York: Springer-Verlag
10. Cole JD. 1968. Perturbation Methods in Applied Mathematics. Waltham: Blaisdell
11. Cole JD. 1994. The development of perturbation theory at GALCIT. SIAM Rev. 36:425-430
12. Colton D. 1979. Arthur Erdélyi. Bull. Lond. Math. Soc. 11:191-207
13. Cornwell J. 2003. Hitler's Scientists. New York: Viking
14. Darrigold O. 2005. Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl. Oxford, UK: Oxford Univ. Press
15. Dauben JW. 1995. Abraham Robinson: The Creation of Nonstandard Analysis, a Personal and Mathematical Odyssey. Princeton, NJ: Princeton Univ. Press
16. De Coster C, Habets P. 2006. Two-Point Boundary Value Problems: Lower and Upper Solutions. Amsterdam: Elsevier
17. Dryden HL. 1955. Fifty years of boundary layer theory and experiment. Science 121:375-380
18. Eckert M. 2006. The Dawn of Fluid Dynamics. Weinheim: Wiley-VCH
19. Eckhaus W. 1997. Witus en de jaren van angst, Een reconstructie. Amsterdam: Bas Lubberhuizen
20. Flügge-Lotz I. Flü gge W. 1973. Ludwig Prandtl in the nineteen-thirties: reminiscences. Annu. Rev. Fluid Mech. 5:1-9
21. Friedrichs KO. 1953. Special Topics in Fluid Mechanics. Lecture Notes. New York: New York Univ.
22. Friedrichs KO. 1955. Asymptotic phenomena in mathematical physics. Bull. Am. Math. Soc. 61:367-381
23. Friedrichs KO, Stoker JJ. 1941. The nonlinear boundary value problem of the buckled plate. Am. J. Math. 63:839-888
24. Friedrichs KO, Wasow W. 1946. Singular perturbations of nonlinear oscillations. Duke Math. J. 13:367-381
25. Germain P. 2000. The 'new' mechanics of fluids of Ludwig Prandtl. In Ludwig Prandtl, ein Führer in der Strömungslehre, ed. GEA Meier, pp. 31-40. Braunschweig: Vieweg
26. Gol'denveizer AL. 1960. Some mathematical problems in the linear theory of thin elastic shells. Russ. Math. Surv. 15(5):1-73
27. Goldstein S. 1930. Concerning some solutions of the boundary layer equations in hydrodynamics. Proc. Camb. Philos. Soc. 26:1-30
28. Goldstein S, ed. 1938. Modern Development in Fluid Dynamics. Oxford: Oxford Univ. Press
29. Goldstein S. 1963. Richard von Mises 1883-1953. In Selected Papers of Richard von Mises, Vol. 1, ed. P Frank et al., pp. ix-xiv. Providence, RI: Am. Math. Soc.
30. Goldstein S. 1969. Fluid mechanics in the first half of this century. Annu. Rev. Fluid Mech. 1:1-28
31. Gorn MH. 1992. The Universal Man: Theodore von Kármán's Life in Aeronautics. Washington, DC: Smithsonian Inst. Press
32. Greenberg JL, Goldstein JR. 1983. Theodore von Kármán and applied mathematics in America. Science 222:1300-1304
33. Hanle PA. 1982. Bringing Aeronautics to America. Cambridge, MA: MIT Press
34. Hirschel EH, Prem H, Madelung G, eds. 2004. Aeronautical Research in Germany: From Lilienthal until Today. Berlin: Springer
35. Holton G. 1988. Thematic Origins of Scientific Thought: Kepler to Einstein. Cambridge, MA: Harvard Univ. Press. Rev. ed.
36. Kaplun S. 1967. Fluid Mechanics and Singular Perturbations, ed. PA Lagerstrom, LN Howard, C-S Liu. New York: Academic
37. Krylov NM, Bogoliubov NN. 1943. Introduction to Nonlinear Mechanics. Princeton, NJ: Princeton Univ. Press
38. Lagerstrom PA. 1988. Matched Asymptotic Expansions. New York: Springer-Verlag
39. Lamb H. 1924. Hydrodynamics. Cambridge, UK: Cambridge Univ. Press. 5th ed.
40. Lienhard JH. 1970. Ludwig Prandtl. In Dictionary of Scientific Biography, ed. CC Gillispie, 11:123-125 New York: Scribner
41. Mac Lane S. 1994. Jobs in the 1930s and the views of George D. Birkhoff. Math. Intell. 16(3):6-7
42. Mac Lane S. 2005. Saunders Mac Lane: A Mathematical Autobiography. Wellesley: A. K. Peters
43. Math. Res. Center. 1970. Studies and Essays Presented to Yu-Why Chen. Taipei: Math. Res. Center, Natl. Taiwan Univ.
44. Mehrtens H, Kingsbury VM. 1989. The Gleichschaltung of mathematical societies in Nazi Germany. Math. Intell. 11:48-60
45. Meier GEA, ed. 2000. Ludwig Prandtl, ein Führer in der Strömungslehre. Vieweg: Braunschweig
46. Meier GEA. 2006. Prandtl's boundary layer concept and the work in Göttingen. See Meier et al. 2006, pp. 1-18
47. Meier GEA, Sreenivasan KR, Heinemann H-J, eds. 2006. IUTAM Symposium on One Hundred Years of Boundary Layer Research. Dordrecht: Springer
48. Morawetz CS, ed. 1968. Kurt Otto Friedrichs Selecta. Boston: Birkhäuser
49. Nohel JA. 1998. Commentary. In Selected Papers of Norman Levinson, Vol. 1, ed. JA Nohel, DH Sattinger, pp. 267-287 Boston: Birkhäuser
50. O'Malley RE Jr. 1991. Singular Perturbation Methods for Ordinary Differential Equations. New York: Springer-Verlag
51. O'Malley RE Jr. 1993. Obituary: Wolfgang R. Wasow. SIAM News, Dec., pp. 2-3
52. Pinl M, Furtmü ller L. 1973. Mathematicians under Hitler. In Year Book of the Leo Baeck Institute, 18:129-182 London: Leo Baeck Inst.
53. Prandtl L. 1905. Ü ber Flü ssigkeits bewegung bei kleiner Reibung. Verh. III Int. Math. Kongr., pp. 484-491 Leipzig: Tuebner
54. Prandtl L. 1948. Mein Weg zu Hydrodynamischen Theorien. Phys. Bl. 4:89-92
55. Prandtl L. 1961. Gesammelte Abhandlungen zur angewandten Mechanik, Hydro-und Aerodynamik, ed. W Tollmien, H Schlichting, H Gortler. Berlin: Springer-Verlag
56. Reid C. 1976. Courantin Gottingen and New York: The Story of an Improbable Mathematician. New York: Springer-Verlag
57. Reingold N. 1981. Refugee mathematicians in the United States of America, 1933-1941: reception and reaction. Ann. Sci. 38:313-338
58. Reissner E. 1949. On the theory of thin elastic shells. In Reissner Anniversary Volume: Contributions to Applied Mechanics, ed. Dep. Aeronaut. Eng. Appl. Mech. Polytech. Inst. Brooklyn, pp. 231-247 Ann Arbor, MI: J. W. Edwards
59. Reissner H. 1912. Spannungen in Kugelschalen (Kuppeln). In Festschrift H. Müller-Breslau, pp, 181-193. Leipzig
60. k i|>. Math. Ann. 109:267-272
61. Rothe E. 1933b. ZurTheorie des Skin-effekts. Z Phys. 83:184-186
62. Rothe E. 1936. Uber asymptotische Entwicklungen bei gewissen nicht-linearen Randwertaufgaben. Comp. Math. 3:310-327
63. Rothe E. 1939. Asymptotic solution of a boundary value problem. Iowa State College J. Sci. 13:369-372
64. Schlichting H, Gersten K. 2000. Boundary Layer Theory. Berlin: Springer. 8th ed.
65. Segal SL. 2003. Mathematicians Under the Nazis. Princeton, NJ: Princeton Univ. Press
66. Siegmund-Schultze R 1997. The emancipation of mathematical research publishing in the United States from German dominance (1878-1945). Hist. Math. 24:135-166
67. Siegmund-Schultze R. 2001. Rockefeller and the Internationalization of Mathematics Between the Two World Wars. Basel: Birkhauser
68. Siegmund-Schultze R 2009. Mathematicians Fleeingfrom Nazi Germany. Princeton, NJ: Princeton Univ. Press
69. Tani I. 1977. History of boundary-layer theory. Annu. Rev. Fluid Mech. 9:87-111
70. Taylor GI. 1973. Memories of von Karman. SIAMRev. 15:447-452
71. Ting L. 2000. Boundary layer theory to matched asymptotics. Z Angew. Math. Mech. 80:845-855
72. Tschen Y-W. 1935. Uber das Verhalten der Losungen einer Folge von Differential gleichungen welche im Limes ausarten. Comp. Math. 2:378-401
73. Van Dyke M. 1994. Nineteenth-century roots of the boundary layer idea. SIAMRev. 36:415-424
74. Verhulst F. 2005. Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics. New York: Springer
75. Vogel-Prandtl J. 1993. Ludwig Prandtl, Ein Lebensbild Erinnerungen. Mitterluugen aus dem Max-Plank-Institut fur Strom. No. 107. Gottingen
76. von Karman T. 1954. Aerodynamics: Selected Topics in Light of Their Historical Development. Ithaca, NY: Cornell Univ. Press
77. von Karman T, Edson L. 1967. The Wind and Beyond: Theodore von Karman, Pioneer in Aviation and Pathfinder in Space. Boston: Little-Brown vonMises R, Friedrichs KO. 1971. Fluid Dynamics. New York: Springer-Verlag
78. Wasow W. 1942. On boundary layer problems in the theory of ordinary differential equations. PhD diss., New York Univ.
79. Wasow WR. 1965. Asymptotic Expansions for Ordinary Differential Equations. New York: Wiley-Interscience
80. Wasow WR. 1985. Linear Turning Point Theory. New York: Springer-Verlag
81. Wasow WR. 1986. Memories of Seventy Years, 1909-1979. Private printing
82. Yamaguti M, Nirenberg L, Mizohata S, Sibuya Y, eds. 1993. Mitio Nagumo Collected Papers. Tokyo: Springer-Verlag