Nonstationary free boundary problem for perfect fluid with surface tension

Hisashi OKAMOTO

doi:10.2969/jmsj/03830381

Hisashi OKAMOTO

Author information

JOURNAL FREE ACCESS

1986 Volume 38 Issue 3 Pages 381-401

DOI https://doi.org/10.2969/jmsj/03830381

Details

Published: 1986 Received: November 29, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) T. B. Benjamin, Lectures on nonlinear wave motion, Lectures in Appl. Math., 15, ed. A. C. Newell, Amer. Math. Soc., Providence, 1974.
2) T. B. Benjamin, The solitary wave with surface tension, Quart. Appl. Math., 40 (1982), 231-234.
3) K. O. Friedrichs, On the derivation of the shallow water theory, Appendix to “The formation of breakers and bores” by J. J. Stoker, Comm. Pure Appl. Math., 1 (1948), 1-87.
4) H. Fujita, H. Okamoto and M. Shoji, On the solutions computed by the boundary element method to a free boundary problem of a circulating perfect fluid, preprint.
5) T. Kano and T. Nishida, Sur les ondes de surface de l'eau avec une justification mathématique des équations des ondes en eau peu profonde, J. Math. Kyoto Univ., 19 (1979), 335-370.
6) T. Kano and T. Nishida, Water waves and Friedrichs expansion, Recent Topics in Nonlinear PDE, Hiroshima, eds. M. Mimura and T. Nishida, Lecture Notes Numer. Appl. Anal., 6, Kinokuniya, Tokyo, 1984, pp. 39-57.
7) H. Ockendon and A. M. Taylor, Inviscid Fluid Flow, Springer, 1983.
8) H. Okamoto, Bifurcation phenomena in a free boundary problem for a circulating flow with surface tension, Math. Methods Appl. Sci., 6 (1984), 215-233.
9) H. Okamoto, Stationary free boundary problems for circular flows with or without surface tension, Proc. Nonlinear PDE in Appl. Sci., U. S.-Japan Seminar, Tokyo, 1982, eds. H. Fujita, P. D. Lax and G. Strang, Lecture Notes Numer. Appl. Anal., 5, Kinokuniya, Tokyo, 1983, pp. 233-251.
10) H. Okamoto, Nonstationary or stationary free boundary problems for perfect fluid with surface tension, Recent Topics in Nonlinear PDE, Hiroshima, eds. M. Mimura and T. Nishida, Lecture Notes Numer. Appl. Anal., 6, Kinokuniya, Tokyo, 1984, pp. 143-154.
11) J. J. Stoker, Water Waves, Interscience, New York, 1957.
12) J. J. Stoker, Bifurcation phenomena in surface wave theory, Bifurcation Theory and Nonlinear Eigenvalue Problems, eds. J. B. Keller and S. Antmann, Benjamin, New York, 1969.
13) H. Yosihara, Gravity waves on the free surface of an incompressible perfect fluid of finite depth, Publ. RIMS Kyoto Univ., 18 (1982), 49-96.
14) H. Yosihara, Capillary-gravity waves for an incompressible ideal fluid, J. Math. Kyoto Univ., 23 (1983), 649-694.
15) E. Zeidler, Bifurcation theory and permanent waves, Applications of Bifurcation theory, ed. P. H. Rabinowitz, Academic press, New York, San Fransisco, London, 1977.

Right : [1] T. B. Benjamin, Lectures on nonlinear wave motion, Lectures in Appl. Math., 15, ed. A. C. Newell, Amer. Math. Soc., Providence, 1974.
[2] T. B. Benjamin, The solitary wave with surface tension, Quart. Appl. Math., 40 (1982), 231-234.
[3] K. O. Friedrichs, On the derivation of the shallow water theory, Appendix to “The formation of breakers and bores” by J. J. Stoker, Comm. Pure Appl. Math., 1 (1948), 1-87.
[4] H. Fujita, H. Okamoto and M. Shoji, On the solutions computed by the boundary element method to a free boundary problem of a circulating perfect fluid, preprint.
[5] T. Kano and T. Nishida, Sur les ondes de surface de l'eau avec une justification mathématique des équations des ondes en eau peu profonde, J. Math. Kyoto Univ., 19 (1979), 335-370.
[6] T. Kano and T. Nishida, Water waves and Friedrichs expansion, Recent Topics in Nonlinear PDE, Hiroshima, eds. M. Mimura and T. Nishida, Lecture Notes Numer. Appl. Anal., 6, Kinokuniya, Tokyo, 1984, pp. 39-57.
[7] H. Ockendon and A. M. Taylor, Inviscid Fluid Flow, Springer, 1983.
[8] H. Okamoto, Bifurcation phenomena in a free boundary problem for a circulating flow with surface tension, Math. Methods Appl. Sci., 6 (1984), 215-233.
[9] H. Okamoto, Stationary free boundary problems for circular flows with or without surface tension, Proc. Nonlinear PDE in Appl. Sci., U. S. -Japan Seminar, Tokyo, 1982, eds. H. Fujita, P. D. Lax and G. Strang, Lecture Notes Numer. Appl. Anal., 5, Kinokuniya, Tokyo, 1983, pp. 233-251.
[10] H. Okamoto, Nonstationary or stationary free boundary problems for perfect fluid with surface tension, Recent Topics in Nonlinear PDE, Hiroshima, eds. M. Mimura and T. Nishida, Lecture Notes Numer. Appl. Anal., 6, Kinokuniya, Tokyo, 1984, pp. 143-154.
[11] J. J. Stoker, Water Waves, Interscience, New York, 1957.
[12] J. J. Stoker, Bifurcation phenomena in surface wave theory, Bifurcation Theory and Nonlinear Eigenvalue Problems, eds. J. B. Keller and S. Antmann, Benjamin, New York, 1969.
[13] H. Yosihara, Gravity waves on the free surface of an incompressible perfect fluid of finite depth, Publ. RIMS Kyoto Univ., 18 (1982), 49-96.
[14] H. Yosihara, Capillary-gravity waves for an incompressible ideal fluid, J. Math. Kyoto Univ., 23 (1983), 649-694.
[15] E. Zeidler, Bifurcation theory and permanent waves, Applications of Bifurcation theory, ed. P. H. Rabinowitz, Academic press, New York, San Fransisco, London, 1977.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!