Local well-posedness for the periodic mKdV in $H^{1/4+}$
  We study the mKdV equation with periodic boundary conditions. We establish low regularity well -posedness in $H^{\frac{1}{4}+}(T)$. The proof involves a non-linear, solution dependent gauge transformation, similar to the one considered in Nakanishi-Takaoka-Tsutsumi. 
Atanas Stefanov
math.AP