On KP-II type equations on cylinders
arXiv:0901.2004 · doi:10.1016/j.anihpc.2009.04.002
Abstract
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.
32 pages
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Cited by in corpus (5)
- Global well-posedness for the KP-II equation on the background of a non localized solution
- Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher
- On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equations
- Bilinear space-time estimates for linearised KP-type equations on the three-dimensional torus with applications
- Global well-posedness of the generalized KP-II equation in anisotropic Sobolev spaces