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

Author(s)

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

Affiliation

^[1] UFG, Dept Matemat, BR-75800000 Jatai, Go - Brazil

^[2] IMECC UNICAMP, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 417, n. 2, p. 660-693, SEP 15 2014.
• Web of Science Citations: 7

Abstract

In this paper we study the initial-value problem associated with the Benjamin-Ono-Zakharov-Kuznetsov equation. We prove that the IVP for such equation is locally well-posed in the usual Sobolev spaces H-s (R-2), s > 2, and in the anisotropic spaces H-s1,H-s2 (R-2), s(2) > 2, s(1) >= s(2). We also study the persistence properties of the solution and local well-posedness in the weighted Sobolev class Z(s,r) = H-s (R-2) boolean AND L-2 ((1 + x(2) + y(2))(tau) dx dy), where s > 2, r >= 0, and s >= 2r. Unique continuation properties of the solution are also established. These continuation principles show that our persistence properties are sharp. (C) 2014 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