Article ID Journal Published Year Pages File Type
4613557 Journal of Differential Equations 2006 24 Pages PDF
Abstract

We investigate the global well-posedness, scattering and blow up phenomena when the 3-D quintic nonlinear Schrödinger equation, which is energy-critical, is perturbed by a subcritical nonlinearity λ1p|u|u. We find when the quintic term is defocussing, then the solution is always global no matter what the sign of λ1 is. Scattering will occur either when the perturbation is defocussing and or when the mass of the solution is small enough and . When the quintic term is focusing, we show the blow up for certain solutions.

Related Topics
Physical Sciences and Engineering Mathematics Analysis