Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/52501
Type: Artigo de periódico
Title: Local and global well-posedness for the 2D generalized Zakharov-Kuznetsov equation
Author: Linares, F
Pastor, A
Abstract: This paper addresses well-posedness issues for the initial value problem (IVP) associated with the generalized Zakharov-Kuznetsov equation, namely, {ut + partial derivative(x)Delta u+ u(k)u(x) = 0, (x, y) is an element of R(2), t > 0, u(x, y, 0) = u(0)(x, y). For 2 <= k <= 7, the IVP above is shown to be locally well posed for data in H(s) (R(2)), s > 3/4. For k >= 8, local well-posedness is shown to hold for data in H(s) (R(2)), s > s(k), where s(k) = 1 - 3/(2k - 4). Furthermore, for k >= 3, if u(0) is an element of H(1) (R(2)) and satisfies parallel to u(0)parallel to(H1) << 1, then the solution is shown to be global in H(1)(R(2)). For k = 2, if u(0) is an element of H(s)(R(2)), s > 53/63, and satisfies parallel to u(0)parallel to(L2) < root 3 parallel to phi parallel to(L2), where phi is the corresponding ground state solution, then the solution is shown to be global in H(s)(R(2)). (C) 2010 Elsevier Inc. All rights reserved.
Subject: Zakharov-Kuznetsov equation
Local well-posedness
Global well-posedness
Country: EUA
Editor: Academic Press Inc Elsevier Science
Rights: fechado
Identifier DOI: 10.1016/j.jfa.2010.11.005
Date Issue: 2011
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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