Abstract
Having the ill-posedness in the range s < − 3 / 4 of the Cauchy problem for the Benjamin equation with an initial H s ( 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 and also that such a well-posed property is globally valid for s ∈ [ − 3 / 4 , ∞ ) .
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