TY - JOUR

T1 - Critical nonlinear Schrödinger equations with data in homogeneous weighted L2 spaces

AU - Li, Chunhua

AU - Hayashi, Nakao

N1 - Funding Information:
We are grateful to an unknown referee for many useful suggestions and comments. One of the authors (C.L.) would like to thank Professor T. Ogawa for his financial support on her stay in Japan. This work is completed during her stay in Japan in Feb. 2014. The work of N.H. is supported by JSPS KAKENHI Grant Numbers 24654034 , 25220702 .

PY - 2014/11/15

Y1 - 2014/11/15

N2 - 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.

AB - 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.

KW - Critical nonlinearities

KW - Nonlinear Schrödinger equations

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U2 - 10.1016/j.jmaa.2014.05.053

DO - 10.1016/j.jmaa.2014.05.053

M3 - Article

AN - SCOPUS:84903464572

VL - 419

SP - 1214

EP - 1234

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -