The Ivp For The Benjamin-ono-zakharov-kuznetsov Equation In Low Regularity Sobolev Spaces

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)In this paper we study the initial-value problem associated with the Benjamin-Ono-Zakharov-Kuznetsov equation. Such equation appears as a two-dimensional generalization of the Benjamin-Ono equation when transverse effects are included via weak dispersion of Zakharov-Kuznetsov type. We prove that the initial value problem is locally well-posed in the usual L-2(R-2)-based Sobolev spaces H-s (R-2), s > 11/8, and in some weighted Sobolev spaces. To obtain our results, most of the arguments are accomplished taking into account the ones for the Benjamin-Ono equation. (C) 2016 Elsevier Inc. All rights reserved.26120412067CNPq [303374/2013-6]FAPESP [2013/08050-7]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP