JournalsaihpcVol. 26, No. 6pp. 2335–2358

On KP-II type equations on cylinders

  • Axel Grünrock

    Rheinische Friedrich-Wilhelms-Universität Bonn, Mathematisches Institut, Beringstraße 1, 53115 Bonn, Germany

  • Mahendra Panthee

    Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal

  • Jorge Drumond Silva

    Center for Mathematical Analysis, Geometry and Dynamical Systems, Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
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Abstract

In this article we study the generalized dispersion version of the Kadomtsev–Petviashvili II equation, on and . 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.

Cite this article

Axel Grünrock, Mahendra Panthee, Jorge Drumond Silva, On KP-II type equations on cylinders. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 6, pp. 2335–2358

DOI 10.1016/J.ANIHPC.2009.04.002