We consider the initial value problem for nonlinear Schrödinger equations with the critical nonlinearities λ1|u|2/nu, 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-n/2 for t>1 if Imλ1=0. The higher uniform time decay rates t-n2(logt)-n2 for t>1 are obtained if Imλ1<0.
- Critical nonlinearities
- Nonlinear Schrödinger equations
ASJC Scopus subject areas
- Applied Mathematics