The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in low regularity Sobolev spaces
Analysis of PDEs
2016-01-13 v1
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 -based Sobolev spaces , , 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.
Keywords
Cite
@article{arxiv.1601.02803,
title = {The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in low regularity Sobolev spaces},
author = {Alysson Cunha and Ademir Pastor},
journal= {arXiv preprint arXiv:1601.02803},
year = {2016}
}