Sharp local well-posedness for a fifth-order shallow water wave equation

In this paper we prove that the already-established local well-posedness in the range s > − 5 / 4 of the Cauchy problem with an initial H s ( R ) data for a fifth-order shallow water wave equation is extendable to s = − 5 / 4 by using the F ¯ s space. This is sharp in the sense that the ill-posedness in the range s < − 5 / 4 of this initial value problem is already known.