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We prove that the "good" Boussinesq model with the periodic boundarycondition is locally well-posed in the space $H^{s}\times H^{s-2}$ for $s >-3/8$. In the proof, we employ the normal form approach, which allows us toexplicitly extract the rougher part of the solution. This also leads to theconclusion that the remainder is in a smoother space $C([0,T], H^{s+a}), where$0 <= a < \min (2s+1, 1/2)$. If we have a mean-zero initial data, this impliesa smoothing effect of this order for the non-linearity. This is new even in thepreviously considered cases $s > -1/4$.

Improved local well-posedness for the periodic "good" Boussinesq equation