The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in low regularity Sobolev spaces

2016/01/12 by Alysson Cunha, Cunha, Alysson, Ademir Pastor +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP

paper · pdf · doi:10.48550/arxiv.1601.02803

arxiv created 2016/01/12 · openalex publication_date 2016/01/12 · arxiv updated 2016/01/13 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

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 L²(\R²)-based Sobolev spaces H^s(\R²), 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.

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