On a model system for the oblique interaction of internal gravity waves

Mathematical Modelling and Numerical Analysis

Volumn 34, Issue 2, 2000, Pages 501-523

  Saut, Jean Claude ^a   Tzvetkov, Nikolay ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Cauchy problem; Internal gravity waves; Kadomtsev Petviashvili equations

Indexed keywords

EID: 0034387149     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2000153     Document Type: Article

References (25)

1. J. Albert, J. Bona and J.C. Saut, Model equations for waves in stratified fluids. Proc. Roy. Soc. Lond. A 453 (1997) 1213-1260.
2. S. Alinhac and P. Gérard, Opérateurs pseudo-différentiel et théorème de Nash-Moser. Éditions du CNRS, EDP Sciences (1991).
3. J.M. Ash, J. Cohen and G. Wang, On strongly interacting internal solitary waves. J. Fourier Anal. and Appl. 5 (1996) 507-517.
4. J. Bona, G. Ponce, J.C. Saut and M. Tom, A model system for strong interaction between internal solitary waves. Comm. Math. Phys. 143 (1992) 287-313.
5. J.-M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Annales de l'ENS 14 (1981) 209-246.
6. J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations I. Schrödinger equations. GAFA 3 (1993) 107-156.
7. J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations II. The KdV equation. GAFA 3 (1993) 209-262.
8. J. Bourgain, On the Cauchy problem for the Kadomtsev-Petviashvili equation. CAFA 3 (1993) 315-341.
9. J.-Y. Chemin, Fluid parfaits incompressibles. Astérisque 230 (1995).
10. R. Coifman and Y. Meyer, Au delà des operateurs pseudodifférentiels. Astérisque 57 (1978).
11. I. Gallagher, Applications of Schochet's methods to parabolic equations. J. Math. Pures Appl. 77 (1998) 989-1054.
12. J.A. Gear and R. Grimshaw, Weak and strong interactions between internal solitary waves. Stud. Appl. Math. 65 (1984) 235-258.
13. J. Ginibre, Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace (d'après Bourgain). Séminaire Bourbaki 796, Astérique 237 (1995) 163-187.
14. J. Ginibre, Y. Tsutsumi and G. Velo, On the Cauchy problem for the Zakharov system. J. Funct. Anal. 151 (1997) 384-436.
15. R. Grimshaw, Y. Zhu, Oblique interactions between internal solitary waves. Stud. Appl. Math. 92 (1994) 249-270.
16. D. Iftimie, The resolution of the Navier-Stokes equations in anisotropic spaces. Revista Matematica Ibero-Americana 15 (1999) 1-36.
17. R.J. Iório Jr, W.V.L. Nunes, On equations of KP-type. Proc. Roy. Soc. Edinburgh A 128 (1998) 725-743.
18. s , s > 0, preprint (1997).
19. 2 global well-posedness of the initial value problem associated to the Benjamin equation. J. Differential Equations 152 (1999) 377-393.
20. C. Kenig, G. Ponce and L. Vega, A bilinear estimate with applications to the KdV equations. J. AMS 9 (1996) 573-603.
21. C. Kenig, G. Ponce and L. Vega, Quadratic forms for 1 - D semilinear Schrödinger equation. Trans. Amer. Math. Soc. 348 (1996) 3323-3353.
22. J.C. Saut, Remarks on the generalized Kadomtsev-Petviashvili equations. Indiana Univ. Math. J. 42 (1993) 1017-1029.
23. R. Strichartz, Restriction of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44 (1977) 705-714.
24. H. Takaoka, Well-posedness for the Kadomtsev-Petviashvili II equation, preprint (1998).
25. N. Tzvetkov, Global low regularity solutions for Kadomtsev-Petviashvili equation. Diff. Int. Eq. (to appear).