We consider the initial value problem for cubic derivative nonlinear Schrödinger 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 \(L^2\).
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Dedicated to Professor Akitaka Matsumura on the occasion of his seventieth birthday
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This work is partly supported by Osaka City University Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics JPMXP0619217849). The work of H. S. is supported by Grant-in-Aid for Scientific Research (C) (No. 17K05322), JSPS.
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Li, C., Nishii, Y., Sagawa, Y. et al. On the derivative nonlinear Schrödinger equation with weakly dissipative structure. J. Evol. Equ. (2020). https://doi.org/10.1007/s00028-020-00634-6
- Cubic derivative nonlinear Schrödinger equation
- Large time behavior
- Weakly dissipative structure
Mathematics Subject Classification