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On the derivative nonlinear Schr\"odinger equation with weakly dissipative structure

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arxiv 2004.12075 v1 pith:OLUIZZX6 submitted 2020-04-25 math.AP

Chunhua Li , Yoshinori Nishii , Yuji Sagawa , Hideaki Sunagawa This is my paper · ORCID
classification math.AP
keywords derivativedissipativeequationnonlinearodingerschrweaklycondition
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abstract

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 $L^2$.

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