Pointwise Decay of solutions to the energy critical nonlinear Schrödinger equations

2022/05/11 by Zihua Guo, Guo, Zihua, Chunyan Huang +3 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2205.05244

openalex publication_date 2022/05/11 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28

Abstract

In this note, we prove pointwise decay in time of solutions to the 3D energy-critical nonlinear Schrödinger equations assuming data in L¹∩ H³. The main ingredients are the boundness of the Schrödinger propagators in Hardy space due to Miyachi \citeMiyachi and a fractional Leibniz rule in the Hardy space. We also extend the fractional chain rule to the Hardy space.

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