Sharp Well-posedness for the Benjamin Equation

Details Sharp Well-posedness for the Benjamin Equation Sharp Well-posedness for the Benjamin Equation

2009-10-27

arxiv.org/abs/0910.5157v1

Mathematics

Analysis of PDEs

28 pages. submitted

Scientific paper

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 $s\in [-3/4,\infty)$.

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