On stability of liquid flow down an inclined plane
Author:
S. M. Sun
Journal:
Quart. Appl. Math. 55 (1997), 375-397
MSC:
Primary 76E30; Secondary 35Q35
DOI:
https://doi.org/10.1090/qam/1447584
MathSciNet review:
MR1447584
Full-text PDF Free Access
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Additional Information
- T. Brooke Benjamin, Wave formation in laminar flow down an inclined plane, J. Fluid Mech. 2 (1957), 554–574. MR 134999, DOI https://doi.org/10.1017/S0022112057000373
C.-S. Yih, Stability of liquid flow down an inclined plane, Phys. Fluids 6, 321–334 (1963)
S. P. Lin, Instability of a liquid film flowing down an inclined plane, Phys. Fluids 10, 308–313 (1967)
G. J. De Bruin, Stability of a layer of liquid flowing down an inclined plane, J. Engrg. Math. 8, 259–270 (1974)
J. M. Floryan, S. H. Davis, and R. E. Kelly, Instabilities of a fluid film flowing down a slightly inclined plane, Phys. Fluids 30, 983–989 (1987)
- S. Chandrasekhar, Hydrodynamic and hydromagnetic stability, The International Series of Monographs on Physics, Clarendon Press, Oxford, 1961. MR 0128226
- C. C. Lin, The theory of hydrodynamic stability, Cambridge, at the University Press, 1955. MR 0077331
- D. H. Sattinger, The mathematical problem of hydrodynamic stability, J. Math. Mech. 19 (1969/1970), 979–817. MR 0261182
- V. I. Yudovich, The linearization method in hydrodynamical stability theory, Translations of Mathematical Monographs, vol. 74, American Mathematical Society, Providence, RI, 1989. Translated from the Russian by J. R. Schulenberger. MR 1003607
- James Serrin, On the stability of viscous fluid motions, Arch. Rational Mech. Anal. 3 (1959), 1–13. MR 105250, DOI https://doi.org/10.1007/BF00284160
- D. J. Benney, Long waves on liquid films, J. Math. and Phys. 45 (1966), 150–155. MR 201125
M. C. Shen, S. M. Sun, and R. E. Meyer, Surface waves on viscous magnetic fluid flow down an inclined plane, Phys. Fluids A 3, 439–445 (1991)
- S. M. Shih and M. C. Shen, Uniform asymptotic approximation for viscous fluid flow down an inclined plane, SIAM J. Math. Anal. 6 (1975), 560–582. MR 388969, DOI https://doi.org/10.1137/0506051
- J. T. Beale, Large-time regularity of viscous surface waves, Arch. Rational Mech. Anal. 84 (1983/84), no. 4, 307–352. MR 721189, DOI https://doi.org/10.1007/BF00250586
- J. Thomas Beale and Takaaki Nishida, Large-time behavior of viscous surface waves, Recent topics in nonlinear PDE, II (Sendai, 1984) North-Holland Math. Stud., vol. 128, North-Holland, Amsterdam, 1985, pp. 1–14. MR 882925, DOI https://doi.org/10.1016/S0304-0208%2808%2972355-7
- Daniel D. Joseph, Stability of fluid motions. I, Springer-Verlag, Berlin-New York, 1976. Springer Tracts in Natural Philosophy, Vol. 27. MR 0449147
- M. Renardy and D. D. Joseph, Hopf bifurcation in two-component flow, SIAM J. Math. Anal. 17 (1986), no. 4, 894–910. MR 846396, DOI https://doi.org/10.1137/0517064
- Yoshiaki Teramoto, On the Navier-Stokes flow down an inclined plane, J. Math. Kyoto Univ. 32 (1992), no. 3, 593–619. MR 1183369, DOI https://doi.org/10.1215/kjm/1250519495
- Takaaki Nishida, Yoshiaki Teramoto, and Htay Aung Win, Navier-Stokes flow down an inclined plane: downward periodic motion, J. Math. Kyoto Univ. 33 (1993), no. 3, 787–801. MR 1239093, DOI https://doi.org/10.1215/kjm/1250519193
T. B. Benjamin, Wave formation in laminar flow down an inclined plane, J. Fluid Mech. 2, 554–574 (1957)
C.-S. Yih, Stability of liquid flow down an inclined plane, Phys. Fluids 6, 321–334 (1963)
S. P. Lin, Instability of a liquid film flowing down an inclined plane, Phys. Fluids 10, 308–313 (1967)
G. J. De Bruin, Stability of a layer of liquid flowing down an inclined plane, J. Engrg. Math. 8, 259–270 (1974)
J. M. Floryan, S. H. Davis, and R. E. Kelly, Instabilities of a fluid film flowing down a slightly inclined plane, Phys. Fluids 30, 983–989 (1987)
S. Chandrasekhar, Hydrodynamics and hydromagnetic stability, Oxford University Press, London, 1961
C. C. Lin, The theory of hydrodynamic stability, Cambridge University Press, London, 1955
D. H. Sattinger, The mathematical problem of hydrodynamic stability, J. Math. Mech. 19, 797–817 (1970)
V. I. Yudovich, The linearization method in hydrodynamical stability theory, Translations of Mathematical Monographs, vol. 74, Amer. Math. Soc., Providence, Rhode Island, 1989
J. Serrin, On stability of viscous fluid motions, Arch. Rational Mech. Anal. 3, 1–13 (1959)
D. J. Benney, Long waves on liquid films, J. Math. Phys. 45, 150–155 (1966)
M. C. Shen, S. M. Sun, and R. E. Meyer, Surface waves on viscous magnetic fluid flow down an inclined plane, Phys. Fluids A 3, 439–445 (1991)
S. M. Shih and M. C. Shen, Uniform asymptotic approximation for viscous fluid flow down an inclined plane, SIAM J. Math. Anal. 6, 560–582 (1975)
J. T. Beale, Large-time regularity of viscous surface waves, Arch. Rat. Mech. Anal. 84, 307–352 (1984)
J. T. Beale and T. Nishida, Large-time behavior of viscous surface waves, Recent topics in Nonlinear PDE, II, North-Holland Math. Stud. 128, North-Holland, Amsterdam-New York, 1985, pp. 1–14
D. D. Joseph, Stability of fluid motions I, Springer-Verlag, New York, 1976
M. Renardy and D. D. Joseph, Hopf bifurcation in two-component flow, SIAM J. Math. Anal. 17, 894–910 (1986)
Y. Teramoto, On the Navier-Stokes flow down an inclined plane, J. Math. Kyoto Univ. 32, 593–619 (1992)
T. Nishida, Y. Teramoto, and H. A. Win, Navier-Stokes flow down an inclined plane: Downward periodic motion, preprint
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Article copyright:
© Copyright 1997
American Mathematical Society