Well-posedness of the Cauchy problem of a water wave equation with low regularity initial data

In this paper we investigate local well-posedness of the IVP of a class of fifth-order nonlinear dispersive equations including the equation of Benney modeling the interaction of short and long water waves. By introducing the modified Sobolev spaces H(s,ω)(R) and the modified Bourgain space Xs,ω,b(R2), and making bilinear estimates in the space Xs,ω,b(R2), we prove that the IVP of this class of equations is locally well-posed in H(s,14)(R) for any s>−14.