TY - JOUR
T1 - L2 -decay rate for the critical nonlinear Schrödinger equation with a small smooth data
AU - Ogawa, Takayoshi
AU - Sato, Takuya
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - We consider the Cauchy problem for the one dimensional nonlinear dissipative Schrödinger equation with a cubic nonlinearity λ| u| 2u, where λ∈ C with Im λ< 0. We show that a relation between L2-decay rate for the solution and a smoothness of the initial data. Our result improves the recent work of Hayashi–Li–Naumkin (Adv Math Phys Art. ID 3702738, 7, 2016) for the decay rate of L2.
AB - We consider the Cauchy problem for the one dimensional nonlinear dissipative Schrödinger equation with a cubic nonlinearity λ| u| 2u, where λ∈ C with Im λ< 0. We show that a relation between L2-decay rate for the solution and a smoothness of the initial data. Our result improves the recent work of Hayashi–Li–Naumkin (Adv Math Phys Art. ID 3702738, 7, 2016) for the decay rate of L2.
UR - http://www.scopus.com/inward/record.url?scp=85080132616&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85080132616&partnerID=8YFLogxK
U2 - 10.1007/s00030-020-0621-3
DO - 10.1007/s00030-020-0621-3
M3 - Article
AN - SCOPUS:85080132616
SN - 1021-9722
VL - 27
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
IS - 2
M1 - 18
ER -