Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418418 | Journal of Mathematical Analysis and Applications | 2014 | 21 Pages |
Abstract
We consider the initial value problem for nonlinear Schrödinger equations with the critical nonlinearities λ1|u|2nu, where Imλ1â¤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 tân2 for t>1 if Imλ1=0. The higher uniform time decay rates tân2(logt)ân2 for t>1 are obtained if Imλ1<0.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Chunhua Li, Nakao Hayashi,