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

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