We consider the generalized Ostrovsky equation utx=u+(up)xx. We show that the equation is locally well posed in Hs, s>3/2 for all integer values of p≥2. For p≥4, we show that the equation is globally well posed for small data in H5∩W3,1 and moreover, it scatters small data. The latter results are corroborated by numerical computations which confirm the heuristically expected decay of ∥Lr~t-(r-2)/(2r). © 2010 Elsevier Inc.
