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arXiv · 2205.05244

Pointwise Decay of solutions to the energy critical nonlinear Schr\"odinger equations

Zihua Guo·Chunyan Huang·Liang Song
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Abstract

In this note, we prove pointwise decay in time of solutions to the 3D energy-critical nonlinear Schr\"odinger equations assuming data in $L^1\cap H^3$. The main ingredients are the boundness of the Schr\"odinger propagators in Hardy space due to Miyachi \cite{Miyachi} and a fractional Leibniz rule in the Hardy space. We also extend the fractional chain rule to the Hardy space.

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Zihua Guo, Chunyan Huang, Liang Song. 2022-05-11. Pointwise Decay of solutions to the energy critical nonlinear Schr\"odinger equations. https://arxiv.org/abs/2205.05244

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