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Type: Artigo de periódico
Title: A note on the 2D generalized Zakharov-Kuznetsov equation: Local, global, and scattering results
Author: Farah, LG
Linares, F
Pastor, A
Abstract: We consider the generalized two-dimensional Zakharov-Kuznetsov equation u(t) + partial derivative(x)Delta u + partial derivative(x)(u(k+1)) = 0, where k >= 3 is an integer number. For k >= 8 we prove local well-posedness in the L-2-based Sobolev spaces H-s(R-2), where s is greater than the critical scaling index s(k) = 1 - 2/k. For k >= 3 we also establish a sharp criteria to obtain global H-1(R-2) solutions. A nonlinear scattering result in H-1(R-2) is also established assuming the initial data is small and belongs to a suitable Lebesgue space. (c) 2012 Elsevier Inc. All rights reserved.
Subject: Local and global well-posedness
Nonlinear scattering
Country: EUA
Editor: Academic Press Inc Elsevier Science
Rights: fechado
Identifier DOI: 10.1016/j.jde.2012.05.019
Date Issue: 2012
Appears in Collections:Unicamp - Artigos e Outros Documentos

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