On persistence properties in fractional weighted spaces
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- by G. Fonseca, F. Linares and G. Ponce PDF
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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 $H^s(\mathbb {R})\cap L^2(|x|^{2r}dx)$, $s, r \in \mathbb {R}$. 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.References
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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
- MR Author ID: 343833
- Email: linares@impa.br
- G. Ponce
- Affiliation: Department of Mathematics, South Hall, Room 6607, University of California, Santa Barbara, California 93106
- MR Author ID: 204988
- Email: ponce@math.ucsb.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 5353-5367
- MSC (2010): Primary 35Q53; Secondary 35B65
- DOI: https://doi.org/10.1090/proc/12665
- MathSciNet review: 3411151