A mathematical justification of the forced Korteweg-de Vries equation for capillary-gravity waves

Kyushu Journal of Mathematics

Volumn 60, Issue 2, 2007, Pages 267-303

  Iguchi, Tatsuo ^a,b  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b KEIO UNIVERSITY   (Japan)

Author keywords

Capillary gravity waves; Forced KdV equation; Long wave approximation

Indexed keywords

EID: 34548238144     PISSN: 13406116     EISSN: None     Source Type: Journal    
DOI: 10.2206/kyushujm.60.267     Document Type: Article

References (21)

1. D. M. Ambrose. Well-posedness of vortex sheets with surface tension. SIAM J. Math. Anal. 35 (2003), 211-244.
2. J. L. Bona and R. Smith. The initial-value problem for the Korteweg-de Vries equation. Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 555-601.
3. J. L. Bona and B.-Y. Zhang. The initial-value problem for the forced Korteweg-de Vries equation. Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), 571-598.
4. M. J. Boussinesq. Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant an liquide contenu dans ce canal des vitesses sensiblement parellies de la surface au fond. J. Math. Pure. Appl. (2) 17 (1872), 55-108 (in French).
5. W. Craig. An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits. Commun. Partial Differ. Equations 10 (1985), 787-1003.
6. H. Hasimoto. Water waves. Kagaku 40 (1970), 401-408 (in Japanese).
7. T. Iguchi. Well-posedness of the initial value problem for capillary-gravity waves. Funkcial. Ekvac. 44 (2001), 219-241.
8. T. Iguchi. A long wave approximation for capillary-gravity waves and an effect of the bottom. Preprint.
9. T. Iguchi. A long wave approximation for capillary-gravity waves and the Kawahara equation. Preprint.
10. T. Kakutani and H. Ono. Weak non-linear hydromagnetic waves in a cold collision free plasma. J. Phys. Soc. Japan. 26 (1969), 1305-1318.
11. T. Kano and T. Nishida. A mathematical justification for Korteweg-de Vries equation and Boussinesq equation of water surface waves. Osaka J. Math. 23 (1986), 389-413.
12. T. Kawahara. Oscillatory solitary waves in dispersive media. J. Phys. Soc. Japan 33 (1972), 260-264.
13. D. J. Korteweg and G. de Vries. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Phil. Mag. 39 (1895), 422-443.
14. V. I. Nalimov. The Cauchy-Poisson problem. Dinamika Splošn. Sredy 18 (1974), 104-210 (in Russian).
15. G. Schneider and C. E. Wayne. The long-wave limit for the water wave problem I. The case of zero surface tension. Comm. Pure Appl. Math. 53 (2000), 1475-1535.
16. G. Schneider and C. E. Wayne. Kawahara dynamics in dispersive media. Physica D 152/153 (2001), 384-394.
17. G. Schneider and C. E. Wayne. The rigorous approximation of long-wavelength capillary-gravity waves. Arch. Ration. Mech. Anal. 162 (2002), 247-285.
18. S. Wu. Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Invent. Math. 130 (1997), 39-72.
19. S. Wu. Well-posedness in Sobolev spaces of the full water wave problem in 3-D. J. Amer. Math. Soc. 12 (1999), 445-495.
20. H. Yosihara. Gravity waves on the free surface of an incompressible perfect fluid of finite depth. Publ. RIMS Kyoto Univ. 18 (1982), 49-96.
21. H. Yosihara. Capillary-gravity waves for an incompressible ideal fluid. J. Math. Kyoto Univ. 23 (1983), 649-694.