Global Existence And Blowup Conditions For A Generalized Davey-Stewartson System

Davey-Stewartson system is a kind of mathematical model which describes the propagation of shallow-water waves in a principal direction under the action of both capillarity and gravity.In this thesis,we mainly study the conditions for the blowup and global existence of a Davey-Stewartson system above the ground state mass-energy and sufficient conditions for the existence of blowup in three-dimensional space.Firstly,we consider the Davey-Stewartson system above the ground state mass-energy with the method of studying the classical nonlinear Schr ¨odinger equation which inspired by Duyckaerts and Roudenko.Specifically,by using the virial identity and GagliardoNirenberg inequality,the threshold conditions for the global existence and blowup of the DaveyStewartson system are obtained.Finally,based on the interpolation inequality,the mechanical analogy of a particle moving in a field with a potential barrier is used to obtain the blowup conditions which are different from the above conclusions.