Exact periodic traveling water waves with vorticity

Comptes Rendus Mathematique

Volumn 335, Issue 10, 2002, Pages 797-800

  Constantin, Adrian ^a   Strauss, Walter ^b  

^a LUND UNIVERSITY   (Sweden)

^b BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038391364     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-073X(02)02565-7     Document Type: Article

References (24)

1. C. Amick, L. Fraenkel, J. Toland, On the Stokes conjecture for the wave of extreme form, Acta Mathematica 148 (1982) 193-214.
2. R.E. Baddour, S.W. Song, The rotational flow of finite amplitude periodic water waves on shear currents, Applied Ocean Research 20 (1998) 163-171.
3. A. Constantin, On the deep water wave motion, J. Phys. A 34 (2001) 1405-1417.
4. A. Constantin, W. Strauss, Exact steady periodic water waves with vorticity, 2002 (in preparation).
5. M. Crandall, P. Rabinowitz, Bifurcation from simple eigenvalues, J. Funct. Anal. 8 (1971) 321-340.
6. M.-L. Dubreil-Jacotin, Sur la détermination rigoureuse des ondes permanentes périodiques d'ampleur finie, J. Math. Pures Appl. 13 (1934) 217-291.
7. F. Gerstner, Theorie der Wellen, Abh. Königl. Böhm. Ges. Wiss., 1802.
8. R. Goyon, Contribution à la théorie des houles, Ann. Fac. Sci. Univ. Toulouse 22 (1958) 1-55.
9. T. Healey, H. Simpson, Global continuation in nonlinear elasticity, Arch. Rat. Mech. Anal. 143 (1998) 1-28.
10. R.S. Johnson, A Modern Introduction to the Mathematical Theory of Water Waves, Cambridge University Press, 1997.
11. G. Keady, J. Norbury, On the existence theory for irrotational water waves, Math. Proc. Cambridge Philos. Soc. 83 (1978) 137-157.
12. H. Kielhöfer, Multiple eigenvalue bifurcation for Fredholm operators, J. Reine Angew. Math. 358 (1985) 104-124.
13. Yu.P. Krasovskii, On the theory of steady-state waves of finite amplitude, USSR Comput. Math. Phys. 1 (1961) 996-1018.
14. T. Levi-Civita, Determinazione rigorosa delle onde irrotazionali periodiche in acqua profonda, Rend. Accad. Lincei 33 (1924) 141-150.
15. G. Lieberman, N. Trudinger, Nonlinear oblique boundary value problems for nonlinear elliptic equations, Trans. Amer. Math. Soc. 295 (1986) 509-546.
16. J.B. McLeod, The Stokes and Krasovskii conjectures for the wave of greatest height, Univ. of Wisconsin M.R.C. Report No. 2041, 1979.
17. A.I. Nekrasov, On steady waves, Izv. Ivanovo-Voznesenk. Politekhn. 3 (1921).
18. P. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal. 7 (1971) 487-513.
19. J. Serrin, A symmetry property in potential theory, Arch. Rat. Mech. Anal. 43 (1971) 304-318.
20. G. Stokes, On the theory of oscillatory waves, Trans. Cambridge Philos. Soc. 8 (1847) 441-455.
21. D. Struik, Détermination rigoureuse des ondes irrotationelles périodiques dans un canal á profondeur finie, Math. Ann. 95 (1926) 595-634.
22. J. Toland, On the existence of a wave of greatest height and Stokes's conjecture, Proc. Roy. Soc. London A 363 (1978) 469-485.
23. J. Toland, Stokes waves, Topological Meth. Nonl. Anal. 7 (1996) 1-48.
24. E. Zeidler, Existenzbeweis für permanente Kapillar/Schwerewellen mit allgemeine Wirbelverteilungen, Arch. Rat. Mech. Anal. 50 (1973) 34-72.