On the well-posedness for the generalized Ostrovsky, Stepanyams and Tsimring equation

In this work we prove that the initial value problem associated with equationut+uxxx-η(Hux+Huxxx)+ukux=0,x∈R,t⩾0,where η>0 and H denotes the usual Hilbert transform, is locally well-posed in Sobolev spaces Hs(R) for s⩾0 and k=1,2,3 and globally well-posed in L2(R).