English

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 L2(R2)L^2(\R^2)-based Sobolev spaces Hs(R2)H^{s}(\R^2), s>11/8s>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.

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}
}