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Type: Artigo de periódico
Author: Esfahani, A
Pastor, A
Abstract: Here we consider results concerning ill-posedness for the Cauchy problem associated with the Benjamin-Ono-Zakharov-Kuznetsov equation, namely, (IVP) {u(t) - Hu(xx) + u(xyy) +u(k)u(x) = 0, (x, y) is an element of R(2), t is an element of R(+), u(x, y, 0) = phi(x, y). For k = 1, (IVP) is shown to be ill-posed in the class of anisotropic Sobolev spaces H(s1, s2) (R(2)), s(1),s(2) is an element of R, while for k >= 2 ill-posedness is shown to hold in H(s1,s2) (R(2)), 2s(1) + s(2) < 3/2 - 2/k. Furthermore, for k = 2,3, and some particular values of s(1), s(2), a stronger result is also established.
Subject: Nonlinear PDE
Cauchy problem
Country: EUA
Editor: Amer Mathematical Soc
Rights: aberto
Identifier DOI: 10.1090/S0002-9939-2010-10532-4
Date Issue: 2011
Appears in Collections:Unicamp - Artigos e Outros Documentos

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