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arXiv · 0910.5157

Sharp Well-posedness for the Benjamin Equation

Wengu Chen·Zihua Guo·Jie Xiao
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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 $s\in [-3/4,\infty)$.

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Wengu Chen, Zihua Guo, Jie Xiao. 2009-10-27. Sharp Well-posedness for the Benjamin Equation. https://arxiv.org/abs/0910.5157

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