Well-posedness result for the Ostrovsky, Stepanyams and Tsimring equation at the critical regularity

Studied here is the Ostrovsky, Stepanyams and Tsimring (OST) equation ut+uxxx−εH(u+uxx)x+uux=0. It is showed that the associated initial value problem is locally analytically well-posed in the critical Sobolev spaces H−3∕2(R). This improves the previous results on this equation in the Sobolev spaces.