On the derivative nonlinear Schr\'odinger equation with weakly dissipative structure
- Resource Type
- Working Paper
- Authors
- Li, Chunhua; Nishii, Yoshinori; Sagawa, Yuji; Sunagawa, Hideaki
- Source
- J. Evol. Equ. 21 (2021), no. 2, 1541-1550
- Subject
- Mathematics - Analysis of PDEs
35Q55, 35B40
- Language
We consider the initial value problem for cubic derivative nonlinear Schr\"odinger equation in one space dimension. Under a suitable weakly dissipative condition on the nonlinearity, we show that the small data solution has a logarithmic time decay in $L^2$.
Comment: 10 pages