Article ID Journal Published Year Pages File Type
6418418 Journal of Mathematical Analysis and Applications 2014 21 Pages PDF
Abstract

We consider the initial value problem for nonlinear Schrödinger equations with the critical nonlinearities λ1|u|2nu, where Imλ1≤0, when the space dimension n=1,2. We prove the global existence of small solutions in homogeneous weighted L2(Rn) spaces. It is shown that the small solutions decay uniformly like t−n2 for t>1 if Imλ1=0. The higher uniform time decay rates t−n2(logt)−n2 for t>1 are obtained if Imλ1<0.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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