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 , and globally well-posed in Hs(R) when s⩾0.