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arXiv · 1405.7909

On persistence properties in fractional weighted spaces

G. Fonseca·F. Linares·G. Ponce
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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.

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G. Fonseca, F. Linares, G. Ponce. 2014-05-30. On persistence properties in fractional weighted spaces. https://arxiv.org/abs/1405.7909

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