On the persistence properties for the fractionary BBM equation with low dispersion in weighted Sobolev spaces

TL;DR

This paper investigates the persistence of polynomial decay in solutions to the low dispersion fractional BBM equation within weighted Sobolev spaces, establishing sharp results and unique continuation properties.

Contribution

It provides the first analysis of persistence properties and sharp decay results for the low dispersion fractional BBM equation in weighted Sobolev spaces.

Findings

Polynomial decay is not preserved by the fBBM flow.

Established local persistence results in weighted Sobolev spaces.

Proved unique continuation results indicating sharpness of persistence properties.

Abstract

We consider the initial value problem associated to the low dispersion fractionary Benjamin-Bona-Mahony equation, fBBM. Our aim is to establish local persistence results in weighted Sobolev spaces and to obtain unique continuation results that imply that those results above are sharp. Hence, arbitrary polynomial type decay is not preserved by the fBBM flow.