On KP-II type equations on cylinders
نویسندگان
چکیده
منابع مشابه
On Kp-ii Type Equations on Cylinders
In this article we study the generalized dispersion version of the Kadomtsev-Petviashvili II equation, on T × R and T × R. 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 equa...
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For a rather general class of equations of Kadomtsev-Petviashvili (KP) type, we prove that the zero-mass (in x) constraint is satisfied at any non zero time even if it is not satisfied at initial time zero. Our results are based on a precise analysis of the fundamental solution of the linear part and its anti x-derivative.
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Article history: Received 11 August 2009 Received in revised form 28 October 2009 Accepted 3 November 2009 Available online 12 November 2009 Communicated by A.P. Fordy
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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 tha...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2009
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2009.04.002