Pointwise decay of solutions to the energy critical nonlinear Schrödinger equations

Zihua Guo,Chunyan Huang,Liang Song

doi:10.1016/j.jde.2023.04.018

Pointwise decay of solutions to the energy critical nonlinear Schrödinger equations

Zihua Guo, Chunyan Huang + Show 1 more

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https://doi.org/10.1016/j.jde.2023.04.018

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Journal: Journal of Differential Equations	Publication Date: Apr 17, 2023
Citations: 2

Affiliation: Monash University, Central University of Finance and Economics, Sun Yat-sen University

#Decay In Time Of Solutions #Fractional Leibniz Rule + Show 8 more

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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 [9] and a fractional Leibniz rule in the Hardy space. We also extend the fractional chain rule to the Hardy space.

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