Some variational principles for problems in hydrodynamic and hydromagnetic stability
Author:
R. C. Di Prima
Journal:
Quart. Appl. Math. 18 (1961), 375-385
MSC:
Primary 76.00
DOI:
https://doi.org/10.1090/qam/116767
MathSciNet review:
116767
Full-text PDF Free Access
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Additional Information
- S. Chandrasekhar, On characteristic value problems in high order differential equations which arise in studies on hydrodynamic and hydromagnetic stability, Amer. Math. Monthly 61 (1954), no. 7, 32–45. MR 66778, DOI https://doi.org/10.2307/2308447
S. Chandrasekhar, The stability of viscous flow between rotating cylinders in the presence of a magnetic field, Proc. Roy. Soc. (London) A216, 293–309 (1953)
- S. Chandrasekhar, On the inhibition of convection by a magnetic field, Philos. Mag. (7) 43 (1952), 501–532. MR 53708
- S. Chandrasekhar, On the inhibition of convection by a magnetic field. II, Philos. Mag. (7) 45 (1954), 1177–1191. MR 64593
- Anne Pellew and R. V. Southwell, On maintained convective motion in a fluid heated from below, Proc. Roy. Soc. London Ser. A 176 (1940), 312–343. MR 3752, DOI https://doi.org/10.1098/rspa.1940.0092
G. I. Taylor, Stability of a viscous liquid contained between two rotating cylinders, Phil. Trans. Roy. Soc. A223, 289–343 (1923)
- S. Chandrasekhar, The stability of viscous flow between rotating cylinders, Mathematika 1 (1954), 5–13. MR 63202, DOI https://doi.org/10.1112/S0025579300000474
L. Collatz, Eigenwerteprobleme und ihre numerische Behandlung, Chelsea Publishing Co., New York, 1948
- Bernard Friedman, Principles and techniques of applied mathematics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1956. MR 0079181
- L. V. Kantorovich and V. I. Krylov, Approximate methods of higher analysis, Interscience Publishers, Inc., New York; P. Noordhoff Ltd., Groningen, 1958. Translated from the 3rd Russian edition by C. D. Benster. MR 0106537
D. L. Harris and W. H. Reid, On orthogonal functions which satisfy four boundary conditions, The Astrophysical J. 3, No. 33, 429–453 (1958).
- Richard C. Di Prima, Application of the Galerkin method to problems in hydrodynamic stability, Quart. Appl. Math. 13 (1955), 55–62. MR 69670, DOI https://doi.org/10.1090/S0033-569X-1955-69670-0
S. Goldstein, The stability of viscous fluid flow under pressure between parallel planes, Proc. Camb. Phil. Soc. 32, 40–54 (1936)
- Frank N. Edmonds Jr., Hydromagnetic stability of a conducting fluid in a circular magnetic field, Phys. Fluids 1 (1958), 30–41. MR 116769, DOI https://doi.org/10.1063/1.1724334
- S. Chandrasekhar and R. J. Donnelly, The hydrodynamic stability of helium II between rotating cylinders. I, Proc. Roy. Soc. London Ser. A 241 (1957), 9–28. MR 88245, DOI https://doi.org/10.1098/rspa.1957.0109
- S. Chandrasekhar, The hydrodynamic stability of helium II between rotating cylinders. II, Proc. Roy. Soc. London Ser. A 241 (1957), 29–36. MR 88246, DOI https://doi.org/10.1098/rspa.1957.0110
- Bernard Budiansky, Pai C. Hu, and Robert W. Connor, Notes on the Lagrangian multiplier method in elasticstability analysis, Tech. Notes Nat. Adv. Comm. Aeronaut. 1948 (1948), no. 1558, 46. MR 0024324
H. Jeffreys, Some cases of instability in fluid motion, Proc. Roy. Soc. (London) A118, 195–208 (1928)
- Bernard Budiansky and Edwin T. Kruszewski, Transverse vibrations of hollow thin-walled cylindrical beams, NACA Tech. Note 1952 (1952), no. 2682, 29. MR 66900
S. Chandrasekhar, On characteristic value problems in high order differential equations which arise in studies of hydrodynamic and hydromagnetic stability, Am. Math. Monthly 61, No. 7, 32–45 (1954)
S. Chandrasekhar, The stability of viscous flow between rotating cylinders in the presence of a magnetic field, Proc. Roy. Soc. (London) A216, 293–309 (1953)
S. Chandrasekhar, On the inhibition of convection by a magnetic field, Phil. Mag. Ser. 7, 43, 501–532 (1952)
S. Chandrasekhar, On the inhibition of convection by a magnetic field II, Phil. Mag. Ser. 7, 45, 1177–1091 (1954)
A. Pellew and R. V. Southwell, On maintained convective motion in a fluid heated from below, Proc Roy. Soc. (London) A176, 312–343 (1940)
G. I. Taylor, Stability of a viscous liquid contained between two rotating cylinders, Phil. Trans. Roy. Soc. A223, 289–343 (1923)
S. Chandrasekhar, The stability of viscous flow between rotating cylinders, Mathematika 1, 5–13 (1954)
L. Collatz, Eigenwerteprobleme und ihre numerische Behandlung, Chelsea Publishing Co., New York, 1948
B. Friedman, Principles and techniques of applied mathematics, John Wiley and Sons, New York, 1956
L. V. Kantorovich and V. I. Krylov, Approximate methods of higher analysis, P. Noordhoff Ltd., Groningen, The Netherlands, 1958
D. L. Harris and W. H. Reid, On orthogonal functions which satisfy four boundary conditions, The Astrophysical J. 3, No. 33, 429–453 (1958).
R. DiPrima, Application of the Galerkin method to problems in hydrodynamic stability, Quart. Appl. Math. 13, 55–62 (1955)
S. Goldstein, The stability of viscous fluid flow under pressure between parallel planes, Proc. Camb. Phil. Soc. 32, 40–54 (1936)
F. N. Edmonds, Hydromagnetic stability of a conducting fluid in a circular magnetic field, The Phys. of Fluids 1, 30–41 (1958)
S. Chandrasekhar and R. Donnelly, The hydrodynamic stability of helium II between rotating cylinders I, Proc. Roy. Soc. 241, 9–28 (1957)
S. Chandrasekhar, The hydrodynamic stability of helium II between rotating cylinders II, Proc. Roy. Soc. 241, 29–36 (1957)
B. Budiansky, P. C. Hu, R. W. Connor, Notes on the Lagrangian multiplier method in elastic-stability analysis, NACA TN 1558 (1948)
H. Jeffreys, Some cases of instability in fluid motion, Proc. Roy. Soc. (London) A118, 195–208 (1928)
B. Budiansky and E. T. Kruszewski, Transverse vibrations of hollow thin-walled cylindrical beams, NACA TR 1129 (1953)
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© Copyright 1961
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