A new criterion and the limit of blowup solutions for a generalized Davey–Stewartson system

Abstract

This paper concerns a generalized Davey–Stewartson system, which is one of the basic models in fluid mechanics. Applying a generalization of Lushnikov’s criteria, a new blowup criterion for a Davey–Stewartson system for the super mass-critical case is obtained. For super mass-critical and sub-cubic cases, we also derive the limit of blowup solutions at the blowup time, which mimics the dynamics of scattering solutions.