On KP-II type equations on cylinders

Details On KP-II type equations on cylinders On KP-II type equations on cylinders

2009-01-14

arxiv.org/abs/0901.2004v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

In this article we study the generalized dispersion version of the Kadomtsev-Petviashvili II equation, on $\T \times \R$ and $\T \times \R^2$. We start by proving bilinear Strichartz type estimates, dependent only on the dimension of the domain but not on the dispersion. Their analogues in terms of Bourgain spaces are then used as the main tool for the proof of bilinear estimates of the nonlinear terms of the equation and consequently of local well-posedness for the Cauchy problem.

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