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Ill-posedness for the Zakharov system with generalized nonlinearity


Authors: H. A. Biagioni and F. Linares
Journal: Proc. Amer. Math. Soc. 131 (2003), 3113-3121
MSC (2000): Primary 35Q55, 35Q51
DOI: https://doi.org/10.1090/S0002-9939-03-06898-9
Published electronically: February 6, 2003
MathSciNet review: 1993221
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Abstract: We study the ill-posedness question for the one-dimensional Zakharov system and a generalization of it in one and higher dimensions. Our point of reference is the criticality criteria introduced by Ginibre, Tsutsumi and Velo (1997) to establish local well-posedness.


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Additional Information

H. A. Biagioni
Affiliation: Departamento de Matemática, IMECC-UNICAMP, 13081-970, Campinas, SP, Brasil
Email: hebe@ime.unicamp.br

F. Linares
Affiliation: Instituto de Matemática Pura e Aplicada, 22460-320, Rio de Janeiro, Brasil
Email: linares@impa.br

DOI: https://doi.org/10.1090/S0002-9939-03-06898-9
Keywords: Ill-posedness, Zakharov system
Received by editor(s): June 15, 2001
Received by editor(s) in revised form: April 28, 2002
Published electronically: February 6, 2003
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2003 American Mathematical Society

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