We give local and global well-posedness results for a system of twoKadomtsev-Petviashvili (KP) equations derived by R. Grimshaw and Y. Zhuto 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. Finallywe extend the result of [3] for lower order perturbationof the system in the absence of transverse effects.
