Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Persistence property in weighted Sobolev spaces for nonlinear dispersive equations


Authors: X. Carvajal and W. Neves
Journal: Quart. Appl. Math. 73 (2015), 493-510
MSC (2010): Primary 35A01, 35Q53
DOI: https://doi.org/10.1090/qam/1387
Published electronically: June 12, 2015
MathSciNet review: 3400755
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Abstract: We generalize the Abstract Interpolation Lemma proved by the authors in Carvajal and Neves (2010). Using this extension, we show in a more general context the persistence property for the generalized Korteweg-de Vries equation in the weighted Sobolev space with low regularity in the weight. The method used can be applied for other nonlinear dispersive models, for instance the multidimensional nonlinear Schrödinger equation.


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X. Carvajal
Affiliation: Instituto de Matemática - Universidade Federal do Rio de Janeiro UFRJ. Av. Athos da Silveira Ramos 149, Centro de Tecnologia Cidade Universitária, Ilha do Fundão, 21941-972 Rio de Janeiro, RJ, Brasil
Email: carvajal@im.ufrj.br

W. Neves
Affiliation: Instituto de Matemática - Universidade Federal do Rio de Janeiro UFRJ. Av. Athos da Silveira Ramos 149, Centro de Tecnologia Cidade Universitária, Ilha do Fundão, 21941-972 Rio de Janeiro, RJ, Brasil
Email: wladimir@im.ufrj.br

DOI: https://doi.org/10.1090/qam/1387
Keywords: Nonlinear dispersive equations, nonlinear Schr\"odinger equation, generalized Korteweg-de Vries equation, initial value problem, weighted Sobolev spaces
Received by editor(s): September 26, 2013
Published electronically: June 12, 2015
Article copyright: © Copyright 2015 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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