Local well-posedness of the Ostrovsky, Stepanyams and Tsimring equation in Sobolev spaces of negative indices

In this paper we prove, by using the method of bilinear estimate in the Bourgain type spaces, that the initial value problem of the OST equation ut+uxxx+η(Hux+Huxxx)+uux=0ut+uxxx+η(Hux+Huxxx)+uux=0 (x∈Rx∈R, t≥0t≥0), where η>0η>0 and HH denotes the usual Hilbert transformation, is locally well-posed in the Sobolev space Hs(R)Hs(R) when s>−1s>−1.