On low regularity of the Ostrovsky, Stepanyams and Tsimring equation

In this paper we prove, by using the Fourier restriction norm method, that the initial value problem of the Ostrovsky, Stepanyams and Tsimring equation u t + u x x x + η ( H u x + H u x x x ) + u u x = 0 ( x ∈ R , t ⩾ 0 ), where η > 0 and H denotes the usual Hilbert transformation, is locally well-posed in the Sobolev space H s ( R ) for any s > − 5 4 , which improve our former result in Zhao and Cui (2009) [5].