Sharp well-posedness of the Ostrovsky, Stepanyams and Tsimring equation

Abstract

In this paper, we study the Ostrovsky, Stepanyams and Tsimring equation. We show that the associated initial value problem is locally well-posed in Sobolev spaces $H^s\left(\mathbb{R}\right)$ for $s>-3/2$. We also prove that our result is sharp in the sense that the flow map of this equation fails to be $C^2$ in $H^s(\mathbb{R})$ for $s<-3/2$.