Abstract
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].
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