Well-posedness of the Cauchy problem for Ostrovsky, Stepanyams and Tsimring equation with low regularity data

In this paper we prove that the initial value problem of the OST equation ut + uxxx + η(Hux + Huxxx) + uux = 0 (x ∈ R, t 0), where η > 0 and H denotes the usual Hilbert transformation, is locally well-posed in the Sobolev space Hs(R) when s >−34 , and globally well-posed in Hs(R) when s 0. © 2008 Elsevier Inc. All rights reserved.