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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Cunha, Alysson [1] ; Pastor, Ademir [2]
Total Authors: 2
[1] UFG, Dept Matemat, BR-75800000 Jatai, Go - Brazil
[2] IMECC UNICAMP, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
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

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 type: Regular Research Grants