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

Zihua Guo; Chunyan Huang; Liang Song

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

Analysis of PDEs 2022-10-19 v2 Classical Analysis and ODEs

Authors: Zihua Guo , Chunyan Huang , Liang Song

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.

Keywords

nonlinear schrödinger equation energy critical pointwise decay hardy space schrödinger propagator fractional leibniz rule

Cite

@article{arxiv.2205.05244,
  title  = {Pointwise Decay of solutions to the energy critical nonlinear Schr\"odinger equations},
  author = {Zihua Guo and Chunyan Huang and Liang Song},
  journal= {arXiv preprint arXiv:2205.05244},
  year   = {2022}
}

Comments

9 pages; In this new version, we extend the fractional chain rule to the Hardy space

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