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arXiv · 2204.07320

Upper and lower $L^2$-decay bounds for a class of derivative nonlinear Schr\"odinger equations

Chunhua Li·Yoshinori Nishii·Yuji Sagawa·Hideaki Sunagawa
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Abstract

We consider the initial value problem for cubic derivative nonlinear Schr\"odinger equations possessing weakly dissipative structure in one space dimension. We show that the small data solution decays like $O((\log t)^{-1/4})$ in $L^2$ as $t\to +\infty$. Furthermore, we find that this $L^2$-decay rate is optimal by giving a lower estimate of the same order.

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Chunhua Li, Yoshinori Nishii, Yuji Sagawa, Hideaki Sunagawa. 2022-04-15. Upper and lower $L^2$-decay bounds for a class of derivative nonlinear Schr\"odinger equations. https://doi.org/10.3934/dcds.2022129

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