Dynamics Of Blow-up Solutions For The Davey-Stewart Son System

The aim of this paper is to study the dynamics of blow-up solutions for the Davey-Stewartson system where u =(l,x):[0,T]×R2→C is the complex valued function and 0<T≤∞,E is singular integral operator.When p=2,for any given points x1,...,Xk in R2,the existence of the blow-up solution is proved in these points.In addition,we investigate the dynamics of blow-up solutions.This result is a complement to the results of F.Merle on the classical Schrodinger equation.Our result gives a rigorous analysis for the numerical result of Besse et al.in[1].When 2<p<∞,by using the profile decomposition theory and variational methods,we firstly derive the concentration of blow-up solutions with bounded Hsc-norm,and then obtain the limiting profile of blow-up solutions.This result is a complement to the results of Li-Zhang-Lai-Wu[19]and Zhu[34]respectively.