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

Author(s)

Cunha, Alysson ^[1] ; Pastor, Ademir ^[2]

Affiliation

^[1] Univ Fed Goias, IME, Caixa Postal 131, BR-74001970 Goiania, Go - Brazil

^[2] Univ Estadual Campinas, IMECC, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Journal of Differential Equations; v. 261, n. 3, p. 2041-2067, AUG 5 2016.
• Web of Science Citations: 4

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 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. (AU)

• FAPESP's process: 13/08050-7 - Nonlinear dispersive evolution equations and applications
• Grantee: Ademir Pastor Ferreira
• Support Opportunities: Regular Research Grants