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

Studied here is the Ostrovsky, Stepanyams and Tsimring (OST) equation u t + u x x x − e H ( u + u x x ) x + u u x = 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.