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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the periodic ``good'' Boussinesq equation


Authors: Luiz Gustavo Farah and Márcia Scialom
Journal: Proc. Amer. Math. Soc. 138 (2010), 953-964
MSC (2000): Primary 35B30; Secondary 35Q55, 35Q72
Published electronically: October 20, 2009
MathSciNet review: 2566562
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Abstract: We study the well-posedness of the initial-value problem for the periodic nonlinear ``good'' Boussinesq equation. We prove that this equation is locally well posed for initial data in Sobolev spaces $ H^s(\mathbb{T})$ for $ s>-1/4$, the same range of the real case obtained by Farah (Comm. Partial Differential Equations 34 (2009), 52-73).


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Additional Information

Luiz Gustavo Farah
Affiliation: Department of Mathematics, Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, C.P. 6065, Campinas, SP, Brazil, CEP 13083-970
Email: lgfarah@gmail.com

Márcia Scialom
Affiliation: Department of Mathematics, Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, C.P. 6065, Campinas, SP, Brazil, CEP 13083-970
Email: scialom@ime.unicamp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10142-9
PII: S 0002-9939(09)10142-9
Received by editor(s): June 22, 2009
Published electronically: October 20, 2009
Additional Notes: The first author was partially supported by FAPESP-Brazil.
Communicated by: Walter Craig
Article copyright: © Copyright 2009 American Mathematical Society