On KP-II type equations on cylinders

Axel Grünrock; Mahendra Panthee; Jorge Drumond Silva

doi:10.1016/j.anihpc.2009.04.002

On KP-II type equations on cylinders

Analysis of PDEs 2015-05-13 v1

Authors: Axel Grünrock , Mahendra Panthee , Jorge Drumond Silva

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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.

Keywords

cauchy problem well-posedness strichartz estimates

Cite

@article{arxiv.0901.2004,
  title  = {On KP-II type equations on cylinders},
  author = {Axel Grünrock and Mahendra Panthee and Jorge Drumond Silva},
  journal= {arXiv preprint arXiv:0901.2004},
  year   = {2015}
}

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32 pages

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