A note on the 2D generalized Zakharov-Kuznetsov equation: Local, global, and scattering results

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:253

Article

Farah, Luiz G.²  Linares, Felipe¹  Pastor, Ademir³ 

[1] IMPA, BR-22460320 Rio De Janeiro, Brazil

[2] Univ Fed Minas Gerais, ICEx, BR-30123970 Belo Horizonte, MG, Brazil

[3] IMECC UNICAMP, BR-13083859 Campinas, SP, Brazil

关键词: Local and global well-posedness;    Nonlinear scattering;   

DOI  :  10.1016/j.jde.2012.05.019

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

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