A note on the Ostrovsky equation in weighted Sobolev spaces

In this work we consider the initial value problem (IVP) associated to the Ostrovsky equations u(t) + partial derivative(3)(x)u +/- partial derivative(-1)(x)u + u partial derivative(x)u = 0, x is an element of R, t is an element of R,} u(x,0) = u(0)(x). We study the well-posedness of the IVP in the weighted Sobolev spaces Z(s,s/2) := {f is an element of H-s (R) : partial derivative(-1)(x) f is an element of L-2(R)}boolean AND L-2(vertical bar x vertical bar(s)dx), with 3/4 < s <= 1. (C) 2017 Elsevier Inc. All rights reserved.