On persistence properties in fractional weighted spaces

G. Fonseca; F. Linares; G. Ponce

On persistence properties in fractional weighted spaces

Analysis of PDEs 2014-06-02 v1

Authors: G. Fonseca , F. Linares , G. Ponce

Abstract

In this work we derive a point-wise formula that will allows us to study the well-posedness of initial value problem associated to nonlinear dispersive equations in fractional weighted Sobolev spaces $H^s(\R)\cap L^2(|x|^{2r}dx)$ , $s, r \in \R$ . 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.

Keywords

persistence properties fractional weighted Sobolev spaces well-posedness nonlinear dispersive equations Korteweg-de Vries equation

Cite

@article{arxiv.1405.7909,
  title  = {On persistence properties in fractional weighted spaces},
  author = {G. Fonseca and F. Linares and G. Ponce},
  journal= {arXiv preprint arXiv:1405.7909},
  year   = {2014}
}

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