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On persistence properties in fractional weighted spaces


Authors: G. Fonseca, F. Linares and G. Ponce
Journal: Proc. Amer. Math. Soc. 143 (2015), 5353-5367
MSC (2010): Primary 35Q53; Secondary 35B65
DOI: https://doi.org/10.1090/proc/12665
Published electronically: June 3, 2015
MathSciNet review: 3411151
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Abstract: In this work we derive a pointwise formula that will allow us to study the well posedness of the initial value problem associated to nonlinear dispersive equations in fractional weighted Sobolev spaces $ H^s(\mathbb{R})\cap L^2(\vert x\vert^{2r}dx)$, $ s, r \in \mathbb{R}$. As an application of this formula we will study local and global well posedness of the $ k$-generalized Korteweg-de Vries equation in these weighted Sobolev spaces.


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Additional Information

G. Fonseca
Affiliation: Departamento de Matemáticas, Universidad Nacional de Colombiam Bogotá, Colombia
Email: gefonsecab@unal.edu.co

F. Linares
Affiliation: IMPA, Instituto Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, RJ, Brazil
Email: linares@impa.br

G. Ponce
Affiliation: Department of Mathematics, South Hall, Room 6607, University of California, Santa Barbara, California 93106
Email: ponce@math.ucsb.edu

DOI: https://doi.org/10.1090/proc/12665
Keywords: Generalized KdV, weighted Sobolev spaces
Received by editor(s): May 22, 2014
Received by editor(s) in revised form: October 9, 2014
Published electronically: June 3, 2015
Additional Notes: The second author was partially supported by CNPq and FAPERJ-Brazil.
The third author was supported by NSF grant DMS-1101499
Communicated by: Catherine Sulem
Article copyright: © Copyright 2015 American Mathematical Society