Nonlinear wave interactions for the benjamin-ono equation

International Mathematics Research Notices

Volumn , Issue 30, 2005, Pages 1833-1847

  Koch, H ^a   Tzvetkov, N ^b  

^a TU DORTMUND UNIVERSITY   (Germany)

^b UNIV LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 24144455954     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/imrn.2005.1833     Document Type: Article

References (17)

1. L. Abdelouhab, J. L. Bona, M. Felland, and J.-C. Saut, Nonlocal models for nonlinear, dispersive waves, Phys. D 40 (1989), no. 3, 360-392.
2. T. B. Benjamin, Internal waves of permanent form in fluids of great depth, J. Fluid Mech. 29 (1967), 559-592.
3. H. A. Biagioni and F. Linares, Ill-posedness for the derivative Schrödinger and generalized Benjamin-Ono equations, Trans. Amer. Math. Soc. 353 (2001), no. 9, 3649-3659.
4. J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II. The KdV-equation, Geom. Funct. Anal. 3 (1993), no. 3, 209-262.
5. _, Periodic Korteweg de Vries equation with measures as initial data, Selecta Math. (N.S.) 3 (1997), no. 2, 115-159.
6. d, Math. Res. Lett. 9 (2002), no. 2-3, 323-335.
7. _, Two singular dynamics of the nonlinear Schrödinger equation on a plane domain, Geom. Funct. Anal. 13 (2003), no. 1, 1-19.
8. M. Christ, J. Colliander, and T. Tao, Ill-posedness for nonlinear Schrödinger and wave equations, preprint, 2003, http://arxiv.org/abs/math.AP/0311048.
9. _, Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations, Amer. J. Math. 125 (2003), no. 6, 1235-1293.
10. G. E. Kenig and K. D. Koenig, On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations, Math. Res. Lett. 10 (2003), no. 5-6, 879-895.
11. C. E. Kenig, G. Ponce, and L. Vega, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc. 9 (1996), no. 2, 573-603.
12. _, On the ill-posedness of some canonical dispersive equations, Duke Math. J. 106 (2001), no. 3, 617-633.
13. s (ℝ), Int. Math. Res. Not. 2003 (2003), no. 26, 1449-1464.
14. L. Molinet, J. C. Saut, and N. Tzvetkov, Ill-posedness issues for the Benjamin-Ono and related equations, SIAM J. Math. Anal. 33 (2001), no. 4, 982-988.
15. G. Ponce, On the global well-posedness of the Benjamin-Ono equation, Differential Integral Equations 4 (1991), no. 3, 527-542.
16. J.-C. Saut, Sur quelques généralisations de l'équation de Korteweg-de Vries, J. Math. Pures Appl. (9) 58 (1979), no. 1, 21-61 (French).
17. 1 (R), J. Hyperbolic Differ. Equ. 1 (2004), no. 1, 27-49.