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

Amin Esfahani

Vol. 18 No. 2 (2013)

Regular Articles

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

Amin Esfahani

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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 $s<-3/2$.

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