On a model system for the oblique interaction of internal gravity waves
Analyse numérique et EDP, Université de Paris-Sud, Bt. 425,
91405 Orsay Cedex, France. (Jean-Claude.firstname.lastname@example.org)
2 Analyse numérique et EDP, Université de Paris-Sud, Bât. 425, 91405 Orsay Cedex, France. (Nikolay.email@example.com )
We give local and global well-posedness results for a system of two Kadomtsev-Petviashvili (KP) equations derived by R. Grimshaw and Y. Zhu to model the oblique interaction of weakly nonlinear, two dimensional, long internal waves in shallow fluids. We also prove a smoothing effect for the amplitudes of the interacting waves. We use the Fourier transform restriction norms introduced by J. Bourgain and the Strichartz estimates for the linear KP group. Finally we extend the result of  for lower order perturbation of the system in the absence of transverse effects.
Mathematics Subject Classification: 35Q07 / 35Q53 / 76B15
Key words: Internal gravity waves / Kadomtsev-Petviashvili equations / Cauchy problem.
© EDP Sciences, SMAI, 2000