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

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.