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

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

2009-01-13

arxiv.org/abs/0901.1807v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

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 $s \ge \frac12$ and $\e > 0$.

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