A-priori bounds for KdV equation below $H^{-3/4}$
  We consider the Korteweg-de Vries Equation (KdV) on the real line, and prove that the smooth solutions satisfy a-priori local in time $H^s$ bound in terms of the $H^s$ size of the initial data for $s\geq -4/5$. 
Baoping Liu
math.AP