A lower bound on the blow-up rate for the Davey-Stewartson system on the   torus
  We consider the hyperbolic-elliptic version of the Davey-Stewartson system with cubic nonlinearity posed on the two dimensional torus. A natural setting for studying blow up solutions for this equation takes place in $H^s, 1/2 < s < 1$. In this paper, we prove a lower bound on the blow up rate for these regularities. 
Nicolas Godet
math.AP