Blow Up Criteria For Two Kinds Of Gross-Pitaevskii Equations

Under the mean field approximation theory,the Gross-Pitaevskii equation is the basic mathematical model used to describe Bose Einstein condensation.In this thesis,we discuss the blow up criterion for the Gross-Pitaevskii equation describing dipole quantum gas and the Gross-Pitaevskii equation with double nonlinear terms.For the Gross-Pitaevskii equation describing the dipole quantum gas,according to the interpolation inequality and means of the mechanical analogy of particle motion in the barrier field,we obtain the blow up criterion for the equation in part of the unstable region.For the Gross-Pitaevskii equation with double nonlinear terms,the blow-up criterion for it is discussed by using the same manners of Weinstein,uncertainty principle and interpolation inequality under different conditions.