Bilinear space-time estimates for linearised KP-type equations on the three-dimensional torus with applications

Abstract

A bilinear estimate in terms of Bourgain spaces associated with a linearised Kadomtsev-Petviashvili-type equation on the three-dimensional torus is shown. As a consequence, time localized linear and bilinear space time estimates for this equation are obtained. Applications to the local and global well-posedness of dispersion generalised KP-II equations are discussed. Especially it is proved that the periodic boundary value problem for the original KP-II equation is locally well-posed for data in the anisotropic Sobolev spaces $H^s_xH^{\e}_y(\T^3)$, if $s\ge \frac{1}{2}$ and $\e > 0$.

13 pages

References in corpus (2)

• Well-posedness and scattering for the KP-II equation in a critical space
• On KP-II type equations on cylinders