On persistence properties in fractional weighted spaces

Fonseca, G.; Linares, F.; Ponce, G.

doi:10.1090/proc/12665

On persistence properties in fractional weighted spaces
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Proc. Amer. Math. Soc. 143 (2015), 5353-5367 Request permission

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.

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