On the Cauchy Problem for the Ostrovsky Equation with Positive Dispersion

Abstract

Abstract In this paper we mainly study the Cauchy problem for the Ostrovsky equation with positive dispersion in the Sobolev space H s of lower order s. Using the crucial bilinear estimates in the Fourier transform restriction spaces related to the Ostrovsky equation, we establish local well-posedness in H s with any and consequently global well-posedness due to the H 1 conservation law. Keywords: Cauchy problemLocal and global well-posednessOstrovsky equationRegularityWeak rotationAMS Subject Classification (2000): 35Q5335A0735B3037K0535B6535B34 Acknowledgment The authors thank the referee for valuable comments.