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

Autor(es)

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

Afiliação do(s) autor(es)

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

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

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 417, n. 2, p. 660-693, SEP 15 2014.
• Citações Web of Science: 7

Resumo

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)

• Processo FAPESP: 13/08050-7 - Equações de evolução dispersivas não-lineares e aplicações
• Beneficiário: Ademir Pastor Ferreira
• Modalidade de apoio: Auxílio à Pesquisa - Regular