Sufficient Conditions For Blowup Solutions Of Several Nonlinear Schr(?)dinger Equations

The nonlinear Schr(?)dinger equation is a basic model of quantum mechanics,which has been widely used in optics,fluid mechanics,quantum mechanics and so on.In this thesis,we discuss the sufficient conditions for the existence of blowup solutions of several nonlinear Schr (?)dinger equations.Firstly,the nonlinear Schr(?)dinger equation in the Bopp-Podolsky electrodynamics is studied.By using virial identities and the Cauchy-Schwartz inequality as well as the uncertainty principle,the variance is analogized to the potential energy of particles moving in a potential barrier field.Then,we obtain sufficient condition for the existence of blowup solutions of this nonlinear Schr(?)dinger equation with arbitrary large initial energy via the convexity of the energy functional for the corresponding mechanical equation.Secondly,we discuss the nonlinear Schr(?)dinger equation with cubic and quintic nonlinearities.Based on the above mechanical analogy method,a sufficient condition for blowup solutions with arbitrary large initial energy is obtained.Furthermore,an interpolation inequality is used to improve the relationship between virial identities and energy-mass.And then,another sufficient condition for blowup solutions of the equation is obtained by mechanical analysis.Finally,we investigate the nonlinear homogeneous Choquard equation above the energymass threshold.On the one hand,we use the Gagliard-Nirenberg inequality,the Pohozaev identity and virial identities to get the sharp condition for global existence and blowup.On the other hand,a new blowup criterion is obtained combining the uncertainty principle and mechanical analysis of particle motion in the barrier field.