Sharp Well-posedness for the Benjamin Equation

Abstract

Having the ill-posedness in the range $s<-3/4$ of the Cauchy problem for the Benjamin equation with an initial $H^s(\mathbb{R})$ data, we prove that the already-established local well-posedness in the range $s>-3/4$ of this initial value problem is extendable to $s=-3/4$ but also that such a well-posed property is globally valid for $s\in [-3/4,\infty )$.

28 pages. submitted

References in corpus (1)

• Decay estimates for a class of wave equations