A lower bound on the blow-up rate for the Davey–Stewartson system on the torus

Abstract

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.