Blow-up for the Davey-Stewartson System with the Subcritical Nonlinearity

    In this talk, we study the two dimensional Davey-Stewartson system in the subcritical case 1 < p < 3. by exploiting a new variational characteristic, we can obtain an increasing order of the subcritical non- linearity by the stability theory for nonlinear schrodingcr equations, and then construct the finite lime blow-up solutions, which suggests the sharp threshold mass of blow-up and global existence for the davey- stewartson system in the case 1 < p < 3. moreover, we give the scaling blow-up rate for the davey-stewartson system without scaling invariance due to 2 < p < 3. and we also find a precisely sharp criteria of blow-up and global existence for the davey-stewartson system in the case 3 < p < +〇〇.